{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Survival Analysis\n",
    "\n",
    "Author: Austin Rochford\n",
    "\n",
    "[Survival analysis](https://en.wikipedia.org/wiki/Survival_analysis) studies the distribution of the time to an event.  Its applications span many fields across medicine, biology, engineering, and social science.  This tutorial shows how to fit and analyze a Bayesian survival model in Python using PyMC3.\n",
    "\n",
    "We illustrate these concepts by analyzing a [mastectomy data set](https://vincentarelbundock.github.io/Rdatasets/doc/HSAUR/mastectomy.html) from `R`'s [HSAUR](https://cran.r-project.org/web/packages/HSAUR/index.html) package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "from pymc3.distributions.timeseries import GaussianRandomWalk\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "from theano import tensor as T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(pm.get_data('mastectomy.csv'))\n",
    "df.event = df.event.astype(np.int64)\n",
    "df.metastized = (df.metastized == 'yes').astype(np.int64)\n",
    "n_patients = df.shape[0]\n",
    "patients = np.arange(n_patients)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>event</th>\n",
       "      <th>metastized</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>23</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>47</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>69</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>70</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>100</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   time  event  metastized\n",
       "0    23      1           0\n",
       "1    47      1           0\n",
       "2    69      1           0\n",
       "3    70      0           0\n",
       "4   100      0           0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "44"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_patients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each row represents observations from a woman diagnosed with breast cancer that underwent a mastectomy.  The column `time` represents the time (in months) post-surgery that the woman was observed.  The column `event` indicates whether or not the woman died during the observation period.  The column `metastized` represents whether the cancer had [metastized](https://en.wikipedia.org/wiki/Metastatic_breast_cancer) prior to surgery.\n",
    "\n",
    "This tutorial analyzes the relationship between survival time post-mastectomy and whether or not the cancer had metastized."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### A crash course in survival analysis\n",
    "\n",
    "First we introduce a (very little) bit of theory.  If the random variable $T$ is the time to the event we are studying, survival analysis is primarily concerned with the survival function\n",
    "\n",
    "$$S(t) = P(T > t) = 1 - F(t),$$\n",
    "\n",
    "where $F$ is the [CDF](https://en.wikipedia.org/wiki/Cumulative_distribution_function) of $T$.  It is mathematically convenient to express the survival function in terms of the [hazard rate](https://en.wikipedia.org/wiki/Survival_analysis#Hazard_function_and_cumulative_hazard_function), $\\lambda(t)$.  The hazard rate is the instantaneous probability that the event occurs at time $t$ given that it has not yet occured.  That is,\n",
    "\n",
    "$$\\begin{align*}\n",
    "\\lambda(t)\n",
    "    & = \\lim_{\\Delta t \\to 0} \\frac{P(t < T < t + \\Delta t\\ |\\ T > t)}{\\Delta t} \\\\\n",
    "    & = \\lim_{\\Delta t \\to 0} \\frac{P(t < T < t + \\Delta t)}{\\Delta t \\cdot P(T > t)} \\\\\n",
    "    & = \\frac{1}{S(t)} \\cdot \\lim_{\\Delta t \\to 0} \\frac{S(t + \\Delta t) - S(t)}{\\Delta t}\n",
    "      = -\\frac{S'(t)}{S(t)}.\n",
    "\\end{align*}$$\n",
    "\n",
    "Solving this differential equation for the survival function shows that\n",
    "\n",
    "$$S(t) = \\exp\\left(-\\int_0^s \\lambda(s)\\ ds\\right).$$\n",
    "\n",
    "This representation of the survival function shows that the cumulative hazard function\n",
    "\n",
    "$$\\Lambda(t) = \\int_0^t \\lambda(s)\\ ds$$\n",
    "\n",
    "is an important quantity in survival analysis, since we may consicesly write $S(t) = \\exp(-\\Lambda(t)).$\n",
    "\n",
    "An important, but subtle, point in survival analysis is [censoring](https://en.wikipedia.org/wiki/Survival_analysis#Censoring).  Even though the quantity we are interested in estimating is the time between surgery and death, we do not observe the death of every subject.  At the point in time that we perform our analysis, some of our subjects will thankfully still be alive. In the case of our mastectomy study, `df.event` is one if the subject's death was observed (the observation is not censored) and is zero if the death was not observed (the observation is censored)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5909090909090909"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.event.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just over 40% of our observations are censored.  We visualize the observed durations and indicate which observations are censored below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "blue, _, red = sns.color_palette()[:3]\n",
    "\n",
    "ax.hlines(patients[df.event.values == 0], 0, df[df.event.values == 0].time,\n",
    "          color=blue, label='Censored')\n",
    "\n",
    "ax.hlines(patients[df.event.values == 1], 0, df[df.event.values == 1].time,\n",
    "          color=red, label='Uncensored')\n",
    "\n",
    "ax.scatter(df[df.metastized.values == 1].time, patients[df.metastized.values == 1],\n",
    "           color='k', zorder=10, label='Metastized')\n",
    "\n",
    "ax.set_xlim(left=0)\n",
    "ax.set_xlabel('Months since mastectomy')\n",
    "ax.set_yticks([])\n",
    "ax.set_ylabel('Subject')\n",
    "\n",
    "ax.set_ylim(-0.25, n_patients + 0.25)\n",
    "\n",
    "ax.legend(loc='center right');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When an observation is censored (`df.event` is zero), `df.time` is not the subject's survival time.  All we can conclude from such a censored obsevation is that the subject's true survival time exceeds `df.time`.\n",
    "\n",
    "This is enough basic surival analysis theory for the purposes of this tutorial; for a more extensive introduction, consult Aalen et al.^[Aalen, Odd, Ornulf Borgan, and Hakon Gjessing. Survival and event history analysis: a process point of view. Springer Science & Business Media, 2008.]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bayesian proportional hazards model\n",
    "\n",
    "The two most basic estimators in survial analysis are the [Kaplan-Meier estimator](https://en.wikipedia.org/wiki/Kaplan%E2%80%93Meier_estimator) of the survival function and the [Nelson-Aalen estimator](https://en.wikipedia.org/wiki/Nelson%E2%80%93Aalen_estimator) of the cumulative hazard function.  However, since we want to understand the impact of metastization on survival time, a risk regression model is more appropriate.  Perhaps the most commonly used risk regression model is [Cox's proportional hazards model](https://en.wikipedia.org/wiki/Proportional_hazards_model).  In this model, if we have covariates $\\mathbf{x}$ and regression coefficients $\\beta$, the hazard rate is modeled as\n",
    "\n",
    "$$\\lambda(t) = \\lambda_0(t) \\exp(\\mathbf{x} \\beta).$$\n",
    "\n",
    "Here $\\lambda_0(t)$ is the baseline hazard, which is independent of the covariates $\\mathbf{x}$.  In this example, the covariates are the one-dimensonal vector `df.metastized`.\n",
    "\n",
    "Unlike in many regression situations, $\\mathbf{x}$ should not include a constant term corresponding to an intercept.  If $\\mathbf{x}$ includes a constant term corresponding to an intercept, the model becomes [unidentifiable](https://en.wikipedia.org/wiki/Identifiability).  To illustrate this unidentifiability, suppose that\n",
    "\n",
    "$$\\lambda(t) = \\lambda_0(t) \\exp(\\beta_0 + \\mathbf{x} \\beta) = \\lambda_0(t) \\exp(\\beta_0) \\exp(\\mathbf{x} \\beta).$$\n",
    "\n",
    "If $\\tilde{\\beta}_0 = \\beta_0 + \\delta$ and $\\tilde{\\lambda}_0(t) = \\lambda_0(t) \\exp(-\\delta)$, then $\\lambda(t) = \\tilde{\\lambda}_0(t) \\exp(\\tilde{\\beta}_0 + \\mathbf{x} \\beta)$ as well, making the model with $\\beta_0$ unidentifiable.\n",
    "\n",
    "In order to perform Bayesian inference with the Cox model, we must specify priors on $\\beta$ and $\\lambda_0(t)$.  We place a normal prior on $\\beta$, $\\beta \\sim N(\\mu_{\\beta}, \\sigma_{\\beta}^2),$ where $\\mu_{\\beta} \\sim N(0, 10^2)$ and $\\sigma_{\\beta} \\sim U(0, 10)$.\n",
    "\n",
    "A suitable prior on $\\lambda_0(t)$ is less obvious.  We choose a semiparametric prior, where $\\lambda_0(t)$ is a piecewise constant function.  This prior requires us to partition the time range in question into intervals with endpoints $0 \\leq s_1 < s_2 < \\cdots < s_N$.  With this partition, $\\lambda_0 (t) = \\lambda_j$ if $s_j \\leq t < s_{j + 1}$.  With $\\lambda_0(t)$ constrained to have this form, all we need to do is choose priors for the $N - 1$ values $\\lambda_j$.  We use independent vague priors $\\lambda_j \\sim \\operatorname{Gamma}(10^{-2}, 10^{-2}).$  For our mastectomy example, we make each interval three months long."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "interval_length = 3\n",
    "interval_bounds = np.arange(0, df.time.max() + interval_length + 1, interval_length)\n",
    "n_intervals = interval_bounds.size - 1\n",
    "intervals = np.arange(n_intervals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see how deaths and censored observations are distributed in these intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.hist(df[df.event == 1].time.values, bins=interval_bounds,\n",
    "        color=red, alpha=0.5, lw=0,\n",
    "        label='Uncensored');\n",
    "ax.hist(df[df.event == 0].time.values, bins=interval_bounds,\n",
    "        color=blue, alpha=0.5, lw=0,\n",
    "        label='Censored');\n",
    "\n",
    "ax.set_xlim(0, interval_bounds[-1]);\n",
    "ax.set_xlabel('Months since mastectomy');\n",
    "\n",
    "ax.set_yticks([0, 1, 2, 3]);\n",
    "ax.set_ylabel('Number of observations');\n",
    "\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the prior distributions on $\\beta$ and $\\lambda_0(t)$ chosen, we now show how the model may be fit using MCMC simulation with `pymc3`.  The key observation is that the piecewise-constant proportional hazard model is [closely related](http://data.princeton.edu/wws509/notes/c7s4.html) to a Poisson regression model.   (The models are not identical, but their likelihoods differ by a factor that depends only on the observed data and not the parameters $\\beta$ and $\\lambda_j$.  For details, see Germán Rodríguez's WWS 509 [course notes](http://data.princeton.edu/wws509/notes/c7s4.html).)\n",
    "\n",
    "We define indicator variables based on whether or the $i$-th suject died in the $j$-th interval,\n",
    "\n",
    "$$d_{i, j} = \\begin{cases}\n",
    "    1 & \\textrm{if subject } i \\textrm{ died in interval } j \\\\\n",
    "    0 & \\textrm{otherwise}\n",
    "\\end{cases}.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "last_period = np.floor((df.time - 0.01) / interval_length).astype(int)\n",
    "\n",
    "death = np.zeros((n_patients, n_intervals))\n",
    "death[patients, last_period] = df.event"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also define $t_{i, j}$ to be the amount of time the $i$-th subject was at risk in the $j$-th interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "exposure = np.greater_equal.outer(df.time, interval_bounds[:-1]) * interval_length\n",
    "exposure[patients, last_period] = df.time - interval_bounds[last_period]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, denote the risk incurred by the $i$-th subject in the $j$-th interval as $\\lambda_{i, j} = \\lambda_j \\exp(\\mathbf{x}_i \\beta)$.\n",
    "\n",
    "We may approximate $d_{i, j}$ with a Possion random variable with mean $t_{i, j}\\ \\lambda_{i, j}$.  This approximation leads to the following `pymc3` model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "SEED = 644567 # from random.org"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    \n",
    "    lambda0 = pm.Gamma('lambda0', 0.01, 0.01, shape=n_intervals)\n",
    "    \n",
    "    beta = pm.Normal('beta', 0, sigma=1000)\n",
    "    \n",
    "    lambda_ = pm.Deterministic('lambda_', T.outer(T.exp(beta * df.metastized), lambda0))\n",
    "    mu = pm.Deterministic('mu', exposure * lambda_)\n",
    "    \n",
    "    obs = pm.Poisson('obs', mu, observed=death)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now sample from the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_samples = 1000\n",
    "n_tune = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [beta, lambda0]\n",
      "Sampling 2 chains: 100%|██████████| 4000/4000 [05:04<00:00, 13.14draws/s]\n",
      "There were 94 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "There were 89 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The number of effective samples is smaller than 25% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = pm.sample(n_samples, tune=n_tune, random_seed=SEED)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the hazard rate for subjects whose cancer has metastized is about double the rate of those whose cancer has not metastized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2134437358971764"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(trace['beta'].mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nSExM5NSpU+zdu5cDBw7w8ccfEx8fT0REBDNmzOD555+npKSEmTNnEh4e3qDXjI6OJjo6us7tIyIiuPfee5k2bRqaptGiRQuSkpKIioqqDTyAWbNmMWvWrNrPEhMTE0lMTGTKlCnMmjWL8MjWVG7+lm/WfMOM6dMcesYFISTghNUwmTW+2niE3m0CiQvxufwK9fDOO+8QFxfHRx99xLPPPouvry8dO3asHYTh5ubGwoULefjhhxk/fjwRERE8/fTTrFq1ij179jRqLRfz73//Gy8vLx577DHKy8sZNGgQc+fOxd39f0eyZrP5rMsLDAYDixYt4u9//zuzZs3ixIkTeAeF4t/vdqY99Uyz1C2EtZI7mQirsTz5OPd9sZV37+jBdV1C9S7HZh04XsKIN1bzzA0dubd/43yOKYSVkTuZCNvy+YZ0QnzdGN4xRO9SbFpciA9dI/yYtzVT7mYiHJoEnLAK6XllrDmYx+29onAxyI/llRqfGEnKsRL2Hi3WuxQhdCN/SYRVmL8tCycFt14VqXcpdmF0Qhiuzk7M25qpdylC6EYCTujOZNZYsD2LAe1a0MqvcS4NcHR+ni5c26kVP+46SqXRdPkVhLBDEnBCd+tS88gpOsWExEvf+UPUz4SeERSWV7M8OffyjYWwQxJwQnfztmXh5+HCsA4yuKQx9YsNJtTPnXnb5DSlcEwScEJXReXVLN17jJu6heHuYtC7HLticFKM6xHB6gMnOF588VnBhbBXEnBCV//dfZQqo5kJPWVwSVMY3zMCswYLt2frXYoQzU4CTuhq/tZM4lv50DncV+9S7FJ0sBdXRQewYHuWXBMnHI4EnNDNgeMl7MoqYkJipNwzsQmN6xFBam4pf2QX6V2KEM1KAk7oZt7WTJydFDd3C9O7FLt2XUIors5OcppSOBwJOKELo8nM9zuOMrRDS4K83S6/gmgwX3cXRnQM4ced2VQZzXqXI0SzkYATulh36CR5pZWM6S7XvjWHcT0iKCivZtV+uSZOOA4JOKGLH3dk4+vuzDXxMtt0cxjQLphgb1c5TSkcigScaHYVVSaW7j3GdV1CcXOWa9+ag7PBiZu6hfNbynEKy6v0LkeIZiEBJ5rdbynHKasyMVoGlzSrsT3CqTZpLNqdo3cpQjQLCTjR7H7YcZQQXzeujgnSuxSH0inMj/hWPizcnqV3KUI0Cwk40awKy6v4/UAuo7uGYXCSa9+a27geEezIKOTwiVK9SxGiyUnAiWa1ZM8xqk0aN3UL17sUh3RTtzCcFHy/QwabCPsnASea1Q87smnTwotOYXJrLj209HVnQLsWLNyejdkst+4S9k0CTjSbo4UVbE7P5+Zu4XJrLh2N7RFOds2+EMKeScCJZrNo11E0DUZ3ldGTehrRsRXebs4y2ETYPQk40Wx+3HmUrpH+RAd76V2KQ/NwNXBdl1b8/McxKqpMepcjRJORgBPN4uDxEpJziuXGylZibI8ISiuNLEs+pncpQjQZCTjRLH7ceRQnBdcnhOpdigB6RQcS7u/BArl1l7BjEnCiyWmaxo+7sukXG0xLH3e9yxGAk5NibI9w1h48wfHiU3qXI0STkIATTW5HZiGZ+RVy7ZuVGdM9HLMGP+6UozhhnyTgRJP7cUc2rs5OXNspRO9SxBnatPCme2t/FmzLRtPkmjhhfyTgRJOqNplZvDuHYR1a4uPuonc54hzjekSwv2YAkBD2RgJONKm1qXmcLKviZjk9aZVuSAjF1eAk88QJuyQBJ5rUDzuy8fNwYXD7lnqXIi7A39OVoR1a8uPObIwms97lCNGoJOBEkymrNLJs73Gu6xKKq7P8qFmrsT0iyCutYs3BPL1LEaJRyV8d0WR+TT5ORbWJMd3l9KQ1GxTXgkAvV+bLrbuEnZGAE03mh53ZhPt7kBgVoHcp4hJcnZ0Y3TWMX5OPU1RRrXc5QjQaCTjRJPJKK1lzMI/R3cJwkolNrd7YHuFUGc0s3n1U71KEaDQScKJJLN51FJNZk9OTNqJLuB/xrXz4bkum3qUI0Wgk4EST+GHnUTqE+hIX4qN3KaIOlFLckhjJrqwiUo7JNXHCPkjAiUaXllfGzsxCxnSXmQNsyc3dw3ExKL7bIoNNhH2QgBON7sed2SgFo7vK6UlbEujlyoiOrfh+RxaVRpknTtg+CTjRqDRN48edR+kdE0QrP5k5wNZMSIygoLya3/bl6l2KEFdMAk40ql1ZRaTllcngEhs1oF0Lwvzc+VYGmwg7IAEnGtUPNTMHjOzSSu9SRAMYnBTje0aw+uAJjhZW6F2OEFdEAk40GqPJch3V0PiW+MrMATZrfM9INA0WbJPBJsK2ScCJRrM2NY+80ipultOTNq11kCd92wbx3bZMzGaZJ07YLgk40WgWbj89c0ALvUsRV+iWxEgy8yvYmHZS71KEaDAJONEoiiqqWbr3GDd1C8PN2aB3OeIKjezcCh93Z7mzibBpEnCiUSzefZRKo5nxPSP0LkU0AncXAzd3C2fJnmNyA2ZhsyTgRKOYtzWL9iE+dAn307sU0UhuSYyk0mjmv7vkBszCNknAiSuWmlvCzsxCJiRGoJTMHGAvOof70iHUV05TCpslASeu2LxtWTg7KRk9aWeUUtyaGMEf2UXsyS7Suxwh6k0CTlwRo8nMwu3ZDG7fkmBvN73LEY1sTI8IPFwMfLXxiN6lCFFvEnDiiqw+eIITJZVMSJTBJfbIz8OF0V3D+HHnUYpPyWATYVsk4MQVmbc1iyAvV4bEt9S7FNFE7ujdmopqE99vz9a7FCHqRQJONFhBWRXL9x2vmUdMfpTsVUKEPwkRfny18QiaJnc2EbZD/iqJBvt+RzbVJk2ufXMAd14dxcHcUrakF+hdihB1JgEnGkTTNL7enEG3SH86hPrqXY5oYjd2DcPX3VkGmwibIgEnGmRLegGpuaXcfnVrvUsRzcDD1cC4nhEs2ZNDXmml3uUIUScScKJB5m7OwMfNmRsSQvUuRTSTO65uTbVJY95WmUZH2AYJOFFvBWVV/PRHDmN6hOPp6qx3OaKZxLb0oXebQL7efESm0RE2QQJO1NuC7VlUGc1yetIB3dk7isz8Cn4/eELvUoS4LAk4US+apjF3cwY9WvsT30oGlziaER1bEeztxn9ksImwARJwol42p+Vz6EQZt/WSozdH5OrsxK1XRbAiJZfswgq9yxHikiTgRL18vTkDH3dnbkgI07sUoZPberVGA77ZnKF3KUJckgScqLP8siqW/HGMcT0i8HCVWbsdVUSAJ0PjWzJ3cwaVRpPe5QhxURJwos6+2ZJBlcnMHTK4xOFN6htNXmkVi3fl6F2KEBclASfqxGgy8+WGI/SPDaZdiI/e5Qid9Y8Npl1Lb+asT5P7UwqrJQEn6mTp3uPkFJ1ict9ovUsRVkApxT39YtiTXczWI3J/SmGdJOBEnXy2Po3WgZ5cI9PiiBpjuofj7+nCnHVpepcixAVJwInL2pNdxJb0Au7uE4XBSeldjrASHq4GJl7VmqV7j8slA8IqScCJy/psfTqergYmJEbqXYqwMnf3iQLgiw3putYhxIVIwIlLyiut5L87jzKuRwR+Hi56lyOsTJi/ByM7tWLupgzKq4x6lyPEWSTgxCXN3WS5NGBS3yi9SxFW6p5+0RSfMrJwe7bepQhxFgk4cVFVRjNfbTrCgHbBxLaUSwPEhfWMCqBLuB+frU+XSwaEVZGAExe1aNdRjhdXMqV/jN6lCCtmuWQgmtTcUtYczNO7HCFqScCJC9I0jY/WHKZ9iA+D41roXY6wctcnhNLCx00uGRBWRQJOXNDqg3mkHCvh/oFtUEouDRCX5uZs4M6ro1i5/wSHT5TqXY4QgAScuIgPVx8ixNeN0V1l1gBRN7df3RpXgxNz1qXrXYoQgAScuIA92UWsSz3JPf1icHWWHxFRNy183BjTPZx52zLJL6vSuxwhJODE+T5acxhvN2dul1kDRD3dPzCGU9VmufBbWAUJOHGWrIJyFu/OYeJVkfi6y4Xdon5iW/owrEMIn69Pp6JK5ooT+pKAE2eZsy4dBXJpgGiwBwe1oaC8mvnbMvUuRTg4CThRq6CsirmbM7ixaxhh/h56lyNsVGJUAN1b+/PRmjRMZrnwW+hHAk7UmrMujfIqE38a3FbvUoQNU0rx4MC2ZOSX88ueY3qXIxyYBJwAoPhUNXPWpzOyUyuZsVtcseEdQ4gJ9uKD1Yfk9l1CNxJwAoAvNxyh5JSRR4bE6l2KsAMGJ8V9A2LYnVXEhsMn9S5HOCgJOEF5lZFP1qZxTfsWdA7307scYSfG9YighY8b76xM1bsU4aAk4ARfb8ogv6xKjt5Eo3J3MfDAgDasSz3JtiMFepcjHJAEnIM7VW3iw9WH6dMmiJ5RgXqXI+zMHb1bE+jlytsrDupdinBAEnAObv62LHJLKnlUjt5EE/B0debe/jGs3H+CP7KK9C5HOBgJOAdWbTLz3qpDdG/tT5+2QXqXI+zU3X2i8HV3ZrYcxYlmJgHnwH7YkU12YQWPDomVKXFEk/Fxd+GefjEsSz5OyrFivcsRDkQCzkGZzBrvrjpEx1BfrmnfUu9yhJ27p1803m7OvL1CRlSK5iMB56B+/iOHtLwyHpGjN9EM/D1duatPFD/9kUNqbone5QgHIQHngExmjbd+O0hsS29GdmqldznCQdw/oA2eLgZeX3ZA71KEg5CAc0CLdh0lNbeUacPa4eQkR2+ieQR6uXL/wDYs2XOMXZmFepcjHIAEnIMxmsy89dtB4lv5cF3nUL3LEQ7mvgFtCPRy5Z9L9+tdinAAEnAOZuGObNLyynhseJwcvYlm5+3mzJ8Gt2Vtah7rU/P0LkfYOQk4B1JlNPPv3w6SEOHH8I4hepcjHNSdvaMI83PnlaX7ZaYB0aQk4BzIvG2ZZBVUMH14nIycFLpxdzEwbVgcuzILWbr3uN7lCDsmAecgTlWbeHtFKj1a+zM4roXe5QgHN7ZHOG1bePHasv0YTWa9yxF2SgLOQXyzOYOcolPMGNFejt6E7pwNTvz12nhSc0uZuyVT73KEnZKAcwAVVSbeWXWIq2MC6Sv3nBRW4tpOIfRpE8Try/ZTWF6ldznCDknAOYCvNh7hREmlHL0Jq6KU4tkbO1JcUc2by+VGzKLxScDZudJKI+/9fogB7YLpFWP/87398MMPJCQk4ObmRkxMDP/6178u2X7atGkopXj88cfPWp6SksLVV1+Nn58fEydOpLS09KznV69eTXh4+HnLL+Szzz5DKXXBtklJSQQHB9d+n56ejlKq9uHj40NiYiLffffdRdt4eXnRtm1b7rjjDtasWXPZeqxJh1Bfbr+6NV9uPML+Y3ILL9G4JODs3Ofr08kvq+Kx4XF6l9Lk1q1bx9ixY+nVqxeLFi1iypQpPPnkk7z55psXbJ+cnMynn36Kr6/vec9NnjyZ2NhYvvvuO5KTk/nHP/5R+5zZbGbatGm89NJLeHt7N0lfXnvtNTZs2MCCBQto164dt956K4sXL75gm59//plnnnmGkydPMnDgQJ577rkmqampzBjeHm83Z2Yt3iuXDYjGpWlaXR/CxhRVVGkJSUu1e+Zs1ruUZjFixAhtwIABZy2bPn26FhAQoFVWVp7XfujQodrf//53LSoqSpsxY0bt8pKSEg3QcnNzNU3TtG+++UZLTEysff7DDz/UevXqpZnN5jrVNWfOHA3QSkpKzntu5syZWlBQUO33aWlpGqAtWrSodpnJZNLi4uK066677qJtTnvmmWc0QFu5cmWdarMWc9Ye1qKeXKz9sidH71KEbahTbskRnB37ZE0aRRXVDnH0BrBz506GDRt21rIRI0ZQUFDAhg0bzlo+f/589u3bx1NPPXXedqqqLAMePDw8APD09KxdVlxczDPPPMNbb73VbJ9nOjk50a1bN9LT0y/bdubMmYSFhfH+++83fWGN6M7eUcSFePP84mTKKo16lyPshAScnSosr+LTtWmM7NSKzuF+epfTLE6dOoWrq+tZy9zc3ADYt29f7bKKigpmzJjByy+/jJeX13nbCQwMJCYmhtmzZ5Ofn8+HH35IYmIiAM8//zzDhg2jd+/e9a7PZDJhNBrPepjNdbsGLD09nVYWqip8AAAb60lEQVStLj/zg8FgYMiQIWzcuLHe9enJ2eDECzd3IbuwQu5TKRqNs94FiKbx4erDlFYZme4gR28AsbGxbNmy5axlmzdvBiA/P7922UsvvURoaCh33nnnRbf1zjvvMGHCBP7v//6Pdu3a8c4775Camsonn3zC7t27G1Sfv7//BZcHBZ1/6YbZbMZoNFJcXMzHH3/M5s2bmT17dp1eJyIiguPHbe8OIb1iApnUJ5rP1qczqnMrrm4jl7SIKyMBZ4dOllby2fp0bkgIo30rH73LaTZTp07loYce4qOPPmL8+PFs3ryZ119/HbAc2QCkpaXx2muvsWLFikueYhw1ahS5ublkZWXRtm1bDAYDo0ePZvr06URERPDOO+/wyiuvAPDUU0/xpz/96bL1rV69uva052kffvghCxcuPK/tTTfdVPu1i4sLjz32GA899NDl/xPApgdqPDGyPStScnliwW5++ctAPFwNepckbJgEnB16//dDnKo2MW1YO71LaVZTpkxh165dPPTQQzzwwAN4enryyiuv8OijjxISYrm59FNPPcWoUaOIj4+nsNAyJ5nZbKayspLCwkL8/Pxqg8/T05O4OMsR8PLly9m1axfffvstu3bt4plnnmH9+vUA9OnTh/79+5OQkHDJ+rp3737eqMtzR0ae9sYbb9C/f398fHyIiYk579TrpWRnZ9f219Z4ujrzyrgEbvtoI/9cup9nb+yod0nChslncHYmt/gUX2w4ws3dw2nbommGsFsrg8HA22+/zYkTJ9i9ezfHjx+v/azs9L/79+9n4cKFBAQE1D4yMzN5++23CQgIIDs7+7ztGo1Gpk2bxquvvoqHhwerVq1iyJAhxMfHEx8fz9ChQ/n9998btS+xsbEkJibSvn37eoWb0WhkxYoV9OnTp1HraU592gZxV+8o5qxPY2t6/uVXEOIi5AjOzry76hBGs8ZfhjrW0duZTgcXwLvvvkvfvn2Jj48H4OOPPz7vguuJEycyaNAgHnroIVq0OP9G1O+//z4BAQHceuuttcvKy8trvy4rK7Oa04KzZs3i6NGjTJ06Ve9SrshTo+JZuT+X6d/tZPGjA/DzcNG7JGGDJODsyNHCCr7elMGEnhFEBZ0/OtDebdy4kbVr19KtWzeKi4uZO3cuS5cuZe3atbVtTo+GPJO7uzuRkZEMHjz4vOcKCgp47rnnWLp0ae2ygQMH8sQTT/Dpp58CsGLFCl5++eXG79Bl7N+/n+DgYKqqqkhLS+Obb77hl19+ISkpiUGDBjV7PY3Jy82ZtyZ249YPNvLE/F28f2dPuc2cqDcJODvy9spUNDQeGRKrdym6cHFx4dtvvyUpKQknJycGDBjAunXr6NKlS4O3OXPmTEaPHk2PHj1ql3Xv3p1XX32Vp59+GrDcUaRr165XXH99nb69mLu7O6GhofTp04fVq1czYMCAZq+lKfSMCuTJkfG8+PM+5qxLZ0r/GL1LEjZG1ePUinWcgxEXlJlfzjWvreK2Xq15/ubOepcjRKPQNI0HvtzGypRcvpvahx6tA/QuSViHOh3OyyATO/HG8gMYnJTDHr0J+6SU4rXxXWnl586jX++QaXVEvUjA2YEDx0v4fkc2k/tGE+Lrrnc5QjQqP08X3r2jBydKKnnk6x1Uywzgoo4k4OzAv5YdwMvVmamD2updihBNIiHCnxfHdGZtah5//36P1YxaFdZNBpnYuF2Zhfyy9xjTh8UR4FX366WEsDUTEiM5crKct1emEh3sxUOD5Q2duDQJOBv32rL9BHi6MKV/tN6lCNHkHhsex5H8cl75JYXWgZ5cnxCqd0nCiskpShu28fBJ1hzM40+DY/Fxlwthhf1zclL8c3wCPaMCmP7dTrbInU7EJUjA2ShN03ht6X5CfN24q0+U3uUI0WzcXQx8dHciEf4e3DNnCzsyCvQuSVgpCTgbtWr/CbYeKeDPQ9vh7iJ3XBeOJdDLla/v702Qtyt3f7qZ3VmFepckrJAEnA0ymzX+uXQ/rQM9uSUxUu9yhNBFKz93vr6/N34eLtz1yWb2Hi3SuyRhZSTgbNDPe3JIzinmseFxuBhkFwrHFe7vwdz7e+PlauDOjzexJ1tCTvyP/HW0MUaTmX8tO0D7EB9u7BqmdzlC6C4y0JOv7++Nh4uB2z7cyOY0GXgiLCTgbMzCHdkczivjsRFxGJzk7upCAEQHezH/ob608HXjrk82sSLluN4lCSsgAWdDKo0m3lp+kK4RfozoaJszNgvRVML8PZj3YB/ahXjzwBfb+HHn+ZPXCsciAWdD5m7KILuwgr9eGy9zYwlxAUHebsy9vzc9owKY9u1OPlx9SG7r5cAk4GxEeZWRt1em0qdNEP1ig/QuRwir5ePuwudTenFd51D+8XMKz/y4B6PcoNkhya26bMScdenklVbxwV3t5ehNiMtwdzEw+7buRAR68MHvh8kuqODt23vg5SZ/8hyJHMHZgKKKaj74/RDDOrSkZ5RM+ChEXTg5Kf42qgMvjunM6oN5THh/A8eKTuldlmhGEnA24MPVhyg+ZWTGiPZ6lyKEzbnj6ig+npTIkZNljHl3HftyivUuSTQTCTgrd6zoFJ+sTWN01zA6hPrqXY4QNuma9i2ZN7UvmgYT3t/A7wdO6F2SaAYScFbuX7/ux2yGv14rR29CXImOYb58/3BfIgM9mfLZFuZuztC7JNHEJOCsWMqxYuZvy+LuPlFEBnrqXY4QNi/Uz4N5U/swoF0wf1v4By/9vA+zWS4jsFcScFbs5SUpeLs588iQWL1LEcJueLs58/HdidzdJ4oPVh9m6lfbKK8y6l2WaAIScFZqXWoeq/af4JEhsfh7uupdjhB2xdngxKybOpN0Y0eW7zvOLR9s4HixjLC0N6oeV/nLcXwzMZs1bnx7LYXl1fw2Y5DM9yZEE1qRcpxHv96Bj7sLn0xOpFOYn94licur08XAcgRnhX7Ymc3eo8U8MbK9hJsQTWxIfAjzpvZFKcsIy+XJcqNmeyEBZ2VKK428vCSFhAg/bkyQ6XCEaA4dw3z58eF+xLb05v4vt/LJ2jS5h6UdkICzMrN/O0huSSWzbuqMk0yHI0SzaenrzrcP9OHajq14fnGy3MPSDkjAWZHU3FI+WZvGLYkRdIv017scIRyOh6uBd+/owdRBbflqYwb3fLaF4lPVepclGkgCzkpomkbSf/fi4WrgiZHxepcjhMNyclI8NSqeV8clsOHQSSa8t4Hswgq9yxINIAFnJZbuPcba1DxmDI8j2NtN73KEcHi3XBXJ51N6cbSogpvfWccfWUV6lyTqSQLOClRUmXh+8T7iW/lwZ+8ovcsRQtToFxvMwof64mpw4pYPNvCrjLC0KRJwVuDN5QfILqzgudGdcDbILhHCmrQL8eGHh/sRF+LNA19uZc66NL1LEnUkf011tiOjgI/WHOa2XpFc3UZm6hbCGrXwceObB/owomMIzy1KJum/ezHJPSytntzJREenqk3cMHst5ZVGlk4fiI+7i94lCSEuwWTWeOnnfXy8No1hHVry1sTuMku4PuROJtburd8OkppbykvjEiTchLABBifF32/oyPM3dWJFSi63friBnCIZYWmtJOB0siuzkA9+P8StiZEMimuhdzlCiHq4q080n0y6irQTZdz09jp2ZhbqXZK4ADlFqYNKo4kb/r2W0ppTk75y9CaETdp/rIR7P9/CiZJKXh2fwE3dwvUuyVHIKUpr9eJP+ziYW8o/xnaRcBPChrVv5cOPD/eja4Q/f/lmJ68v2y8TqFoRCbhmtnj3Ub7YcIT7B8RwTfuWepcjhLhCQd5ufHXf1dyaGMnsFan86T/bZQJVKyGnKJtRam4pN7+zjnYh3nz3YB9c5Jo3IeyGpml8ui6dF39KJi7Ehw/u6klUkJfeZdkrOUVpTYoqqnngi624OTsx+7bu/POVl4mMjMTDw4OBAweyc+fOy27j119/5bbbbiM6OhqlFElJSU1fuBB2IDU1lQcffJCuXbtiMBgYPHhwndbbunUrI0aMICgoiMDAQIYNG8amTZsu2FYpxb39Y5hzTy9yik5xw+y1MrecziTgmoHJrDHtmx1k5Jfz7h09+PL9t3j++ed58sknWbRoEd7e3gwbNoxjx45dcju//PILu3fvZujQoXh6ejZT9ULYvr179/Lzzz8TFxdHXFxcndbJzMxk2LBhGI1GvvjiC7788kuMRiMjRozgyJEjF11vUFwLFj/an6ggT+77YiuvLd0vF4XrRdO0uj5EA5jNZu1vC3drUU8u1r7ckK5VVFRovr6+2nPPPVfbprS0VAsODtaefvrpS27LZDLVfh0UFKTNnDmzqcoWwq6c+bszbtw4bdCgQZdd57333tOcnJy0goKC2mX5+fmak5OT9u677152/Yoqo/bEvF1a1JOLtTs/3qidLK1sUO3iguqUW3IE18Rmr0jl600ZTB3Uljt7R7F+/XqKi4u55ZZbatt4eXlx4403smTJkktuy8lJdpcQDdGQ353q6mqcnZ3x9vauXebt7Y2zs3OdZvt2dzHwyvgEXh7bhU1p+dw4ey07MgrqXYdoOPmL2YQ+Wn2Yf/16gLHdw3lyZHsAUlJSMBgMtGvX7qy2HTp0ICUlRY8yhRAXMG7cODw9PZkxYwa5ubnk5uYyffp0AgICmDBhQp23M7FXaxZM7QvA+Pc3MPu3g3LKsplIwDWRj1Yf5sWf93F9Qiivjk9AKcugn4KCAry9vTEYDGe1DwgIoLy8nKqqKj3KFUKcIywsjJUrV7JgwQJCQkIICQlh4cKFLF26lBYt6nf3oS4Rfvz8lwHckBDK678e4NYPNpCZX95ElYvTJOAamaZp/HNpCi/+vI/rOrfi9XGdQTNjNBoxmUwAtWF37noXe04I0fxycnIYP348PXv2ZMmSJSxZsoSePXty/fXXk5GRUe/t+Xm48NbE7rx5azf2HyvhurfW8N3WzDqd7hQNIwHXiCqNJp6Yv5t3Vh7itl6RjAstwsPdDRcXF1xcXBg6dCgBAQGUlJTUht1phYWFeHp64uIidzYRwhr885//xGg0Mn/+fEaOHMnIkSNZsGABBoOB1157rcHbvbl7OD//ZQAdwnx5Yv5uJs/ZwtFCuWFzU5B5HhpJbvEppn61je0Zhfx5aDumD2tHaWkpW7ZsqW3j4+NDdnY2JpOJ1NRU2rdvX/tcSkoK8fHxepQuhLiAlJQUOnXqdNabTldXVzp16sShQ4euaNuRgZ58c39vvtx4hJeXpHDtG6t5+voO3HpVpJzFaURyBNcIVqbkct2/17Avp4R3bu/BY8PjUErh4+NDYmJi7aN9+/b07dsXX19f5s2bV7t+eXk5ixYtYtSoUTr2QghxpqioKPbs2XPW5+KVlZXs2bOH6OjoK96+k5NiUt9olk4bSKdwX55a+AcT3t9A8tHiK962sDDU424YdW7oKIrKq3l+cTLP/7SP1oGefD6lF33aXnpWbmdny0Hziy++iL+/PyUlJTz22GNkZWXx+eef1w5J/uKLL+jZsyeTJk3C398fgCNHjrB8+XKSk5NZuHAhfn5+KKU4cuTIeaMyhRD/U15ezo8//khycjJLly6loKCAkJAQkpOTiY6OxsXFhdjYWHbt2sVNN90EQGhoKG+88QZbt27F39+fAwcOMGPGDHbv3s0HH3xAq1atGqU2P08XxnaPINzfg0W7c/h0XRr5ZVX0iArA3cVw+Q04pufq1KquF8w14wV8Vs9sNmvzt2ZqPWYt02KeWqw9v2ivVlFlrNf6L7zwghYeHq65u7tr/fv317Zv335Wmzlz5miAlpaWdt6ycx9RUVGN1DMh7FNaWtoFf3fO/B2LiorSJk2adNZ6y5cv1wYMGKAFBARoAQEB2sCBA7WVK1c2WZ2FZVXaMz/8ocU8tVjrPmuZ9tm6NK2y2nT5FR1PnXJLbrZcT3uyi5i1OJnNafl0b+3PCzd3plOYn95lCSHsyN6jRTy/OJmNh/OJDvLkr9fGc12XVvL53P/U6T9CAq6O/sgq4q3fDrB8Xy5+Hi48NSqeWxMjcXKSHzghROPTNI1V+0/w0pJ9HDheSkKEH48OacewDi0l6CTgrpymaWw8nM/Haw7zW0ouvu7O3DegDZP7RctEpUKIZmEyayzYnsXsFQfJzK8gvpUPjwyJZVTnUAyO+wZbAq6hSiuNfL89iy83HuHA8VL8PV24t18MkyTYhBA6MZrM/HfXUd5emcrhE2VEBXlyV+8oJvSMxM/T4f4uScDVh8mssf5QHj/sOMove3IoqzLROdyXu/tEM7prmIxmEkJYBZNZ45c9x5izLo2tRwrwcDFwc/dwbusVSZdwP0c5fSkBdznVJjNb0vNZtvc4P/2Rw4mSSnzcnBnVpRUTe7Wme6S/o/ywCCFs0J7sIr7ccIQfdmZTaTTTpoUXY7qFc3P3cCID7XrOSAm4CzlefIqNh0+yMiWXlftPUFRRjauzE9e0b8HN3cK5Jr6lHK0JIWxKUXk1S/bk8P2ObDal5QPQMdSXIfEtuSa+Jd0i/e3t8zoJuCqjmYO5JSQfLWZ7RiGbDp/kcF4ZAAGeLgyJD2F4xxAGtAvGy03uWiaEsH1ZBeUs3p3Din25bMsowGTWCPB04eqYIHrFBNIrJpAOob62Hnj2HXCaplFaaaSwvJrC8mryyirJLqggs6CcrIIK0k6UcTC3hGqTpWwfd2d6RQfSu00QvdsE0THM5newEEJcUlF5Nb8fPMHv+0+wOf0kmfmWmzp7uRroEOpLh1BfOob5EhfiQ+tAT4K9XW3lYxnrDLgvNqTz798Oomk1txHQNDTAbLb8yznLLe00y79nfG3WNC40Z6CrwYnwAA9aB3rSMcyXjjU7MDrISwJNCOHQcooq2JyWz/YjBezLKSE5p5jSSmPt8x4uBloHehIZ6ElkoAdhfh4E+7gS7O1GsLcbLXzcCPB0tYa/pdYZcKsPnOCXvcdQgFKgUDip/82DdnqZ5d+a75U6b7mTUvh6OOPv6UqApyuBXi5EBHjSwttNLr4WQog6MJs1sgoqOJhbQmZ+ORn5lrNglq/LKa8ynbeOkwIvN2e8XJ3xdDPg7eaMp6sBL1dnvNyc8XAx4OKscDE44WJwwtnJ8nWQtyt394lurNKtM+DEpb3++uskJSVRWlqqdylCOBxvb2+SkpKYMWOG3qXoTtM0SiqN5JVUcqKkkrzSKvJKK8krraS00khZpZGyKhPllUbKKk2UVRkprzJRVmnEaNaoNpmpNpkxmjSMZo3oIE9W/fWaxipPAs4WhYWFkZOTo3cZQjis0NBQjh49qncZdkXTLCHnYmi0GdrqFHAyH5yVmTFjRu2UOUKI5uXt7S1Hb01AKdWY4Vb315UjOCGEEDZGjuCEEEI4Lgk4IYQQdkkCTgghhF2SgBNCCGGXJOCEEELYJQk4IYQQdkkCTgghhF2SgBNCCGGXJOCEEELYJQk4IYQQdkkCTgghhF2SgBNCCGGX6nyz5eeee+4XILhpy2l0YYAjzXsh/bVvjtRfR+orSH/rK2/mzJkjL9tK0zS7fSQlJWl61yD9lf5Kf6Wv0l99+iunKIUQQtglew+45/QuoJlJf+2bI/XXkfoK0t8mUZ8JT4UQQgibYe9HcEIIIRyUBJwQQgi7JAEnhBDCLtlVwCml3JRSs5VSeUqpMqXUf5VSEZdZJ0kppZ3zONZcNdeHUupPSqk0pdQppdQ2pdSAy7QfVNPulFLqsFJqanPV2hjq01+l1OAL7EdNKRXfnDU3hFJqYM3PanZNzZPrsE4XpdTvSqmKmvWeVUqpZij3itW3v0qp6Ivs28tfB6UzpdTflFJblFLFSqkTSqlFSqnOdVjPJvdvQ/rblPvXrgIOeBMYB9wGDAB8gcVKKcNl1tsPhJ7x6NKURTaEUupW4C3gH0B3YD2wRCnV+iLtY4Cfa9p1B14CZiulxjVPxVemvv09QyfO3pcHm7LORuIN7AH+AlRcrrFSyhf4FTgOXAX8Gfgr8FgT1tiY6tXfM4zk7H27ovFLa3SDgXeBvsAQwAgsV0oFXmwFG9+/g6lnf8/Q+PtX7wv+GusB+AFVwB1nLIsEzMC1l1gvCdijd/116N8m4KNzlh0EXrpI+1eAg+cs+xjYoHdfmqi/gwENCNa79ivsdykw+TJtHgKKAY8zlv0dyKZmZLStPOrY3+iafZuod72N0F9vwATc6CD7ty79bbL9a09HcD0BF2DZ6QWapmUC+7C8m7iUNjWnAdKUUt8opdo0YZ31ppRyxdK/Zec8tYyL963PBdovBRKVUi6NW2HjamB/T9uqlMpRSv2mlLqmSQrUXx9gjaZpZx79LMVy+6NoXSpqHguVUrlKqXVKqfF6F9NAPljOnBVcoo097d+69Pe0Rt+/9hRwrbC8U8g7Z/nxmucuZhMwGRgF3F/Tdr1SKqgJamyoYMCApS9nulTfWl2kvTPWf0/RhvQ3B8s733HAWCynnX9TSg1sqiJ1dLF9e/o5e1MKPA7cAlwH/AZ8q5S6U9eqGuYtYCew4RJt7Gn/1qW/TbZ/na90A01NKfUC8PRlml3qnbrCcvh7QZqmLTnn9TYCh4FJwL/qWGZzObcfl+zbRdpfaLm1qnN/NU3bjyXUTtuglIrG8ouzuimK05mt79s60zQtD3j9jEVblVLBwBPAV/pUVX9KqX8B/YH+mqaZLtPc5vdvXfvblPvXFo7g3gQ6XOaxGTiG5V3/uUcnLTn/3dBFaZpWCuwF2l1p4Y0oD8vR6bnv3i7Vt2MXaW8ETjZqdY2vIf29kE1Y135sLBfbt1C//x9bZlP7Vin1BpbBb0M0TTt8meY2v3/r2d8LaZT9a/UBp2lanqZpKZd5lAPbgGpg+Ol1ay4R6IBlBF6dKKXcgXgsp7ysgqZpVVj6N/ycp4Zz8b5tAIZdoP1WTdOqG7fCxtXA/l5IN6xoPzaiDcCAmp/V04ZjmX4kXZeKmp/N7Ful1FvA7Vj+2KfUYRWb3r8N6O+FNM7+1XuUTSOP2HkPy0ijYViGlq/Ecv7XcEabFOCRM75/DRgExABXA4uxjGCK0rs/5/TtViyjRO/DEtpvYTl3HVXz/BfAF2e0jwHK+N8R8H0164/Tuy9N1N9pwM1Y3vV1wnJZhAaM1bsvdeird80vdDegHHi25uvWNc+/BPx2Rns/LO/yvwE6Y/nMsRiYoXdfmqi/k7D8wewAtMdy2rkKmK53X+rQ13dq9s0QLEdlpx/eZ7Sxm/3bwP422f7V/T+kkf9z3YHZWE7BlQOLgMhz2mhA0hnff4PlnVEVlnBcAHTUuy8X6d+fsLyDq8RyhDPwjOdWAavOaT8I2F7TPg2Yqncfmqq/WM7Xp2K5riofWANcp3cf6tjPwTU/l+c+Pqt5/jMg/Zx1umD5bPEUlne6M7GRIeT17W/NH8BkLG/YioGtwJ1696OOfb1QP8/9G2Q3+7ch/W3K/SuzCQghhLBLVv8ZnBBCCNEQEnBCCCHskgScEEIIuyQBJ4QQwi5JwAkhhLBLEnBCCCHskgScEEIIuyQBJ4QQwi5JwAkhhLBL/w/h832NrbiZggAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace, var_names=['beta'], color='#87ceeb');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 993.6x331.2 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.autocorrplot(trace, var_names=['beta']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now examine the effect of metastization on both the cumulative hazard and on the survival function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "base_hazard = trace['lambda0']\n",
    "met_hazard = trace['lambda0'] * np.exp(np.atleast_2d(trace['beta']).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cum_hazard(hazard):\n",
    "    return (interval_length * hazard).cumsum(axis=-1)\n",
    "\n",
    "def survival(hazard):\n",
    "    return np.exp(-cum_hazard(hazard))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_with_hpd(x, hazard, f, ax, color=None, label=None, alpha=0.05):\n",
    "    mean = f(hazard.mean(axis=0))\n",
    "    \n",
    "    percentiles = 100 * np.array([alpha / 2., 1. - alpha / 2.])\n",
    "    hpd = np.percentile(f(hazard), percentiles, axis=0)\n",
    "    \n",
    "    ax.fill_between(x, hpd[0], hpd[1], color=color, alpha=0.25)\n",
    "    ax.step(x, mean, color=color, label=label);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (hazard_ax, surv_ax) = plt.subplots(ncols=2, sharex=True, sharey=False, figsize=(16, 6))\n",
    "\n",
    "plot_with_hpd(interval_bounds[:-1], base_hazard, cum_hazard,\n",
    "              hazard_ax, color=blue, label='Had not metastized')\n",
    "plot_with_hpd(interval_bounds[:-1], met_hazard, cum_hazard,\n",
    "              hazard_ax, color=red, label='Metastized')\n",
    "\n",
    "hazard_ax.set_xlim(0, df.time.max());\n",
    "hazard_ax.set_xlabel('Months since mastectomy');\n",
    "\n",
    "hazard_ax.set_ylabel(r'Cumulative hazard $\\Lambda(t)$');\n",
    "\n",
    "hazard_ax.legend(loc=2);\n",
    "\n",
    "plot_with_hpd(interval_bounds[:-1], base_hazard, survival,\n",
    "              surv_ax, color=blue)\n",
    "plot_with_hpd(interval_bounds[:-1], met_hazard, survival,\n",
    "              surv_ax, color=red)\n",
    "\n",
    "surv_ax.set_xlim(0, df.time.max());\n",
    "surv_ax.set_xlabel('Months since mastectomy');\n",
    "\n",
    "surv_ax.set_ylabel('Survival function $S(t)$');\n",
    "\n",
    "fig.suptitle('Bayesian survival model');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the cumulative hazard for metastized subjects increases more rapidly initially (through about seventy months), after which it increases roughly in parallel with the baseline cumulative hazard.\n",
    "\n",
    "These plots also show the pointwise 95% high posterior density interval for each function.  One of the distinct advantages of the Bayesian model fit with `pymc3` is the inherent quantification of uncertainty in our estimates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Time varying effects\n",
    "\n",
    "Another of the advantages of the model we have built is its flexibility.  From the plots above, we may reasonable believe that the additional hazard due to metastization varies over time; it seems plausible that cancer that has metastized increases the hazard rate immediately after the mastectomy, but that the risk due to metastization decreases over time.  We can accomodate this mechanism in our model by allowing the regression coefficients to vary over time.  In the time-varying coefficent model, if $s_j \\leq t < s_{j + 1}$, we let $\\lambda(t) = \\lambda_j \\exp(\\mathbf{x} \\beta_j).$  The sequence of regression coefficients $\\beta_1, \\beta_2, \\ldots, \\beta_{N - 1}$ form a normal random walk with $\\beta_1 \\sim N(0, 1)$, $\\beta_j\\ |\\ \\beta_{j - 1} \\sim N(\\beta_{j - 1}, 1)$.\n",
    "\n",
    "We implement this model in `pymc3` as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as time_varying_model:\n",
    "    \n",
    "    lambda0 = pm.Gamma('lambda0', 0.01, 0.01, shape=n_intervals)\n",
    "    beta = GaussianRandomWalk('beta', tau=1., shape=n_intervals)\n",
    "    \n",
    "    lambda_ = pm.Deterministic('h', lambda0 * T.exp(T.outer(T.constant(df.metastized), beta)))\n",
    "    mu = pm.Deterministic('mu', exposure * lambda_)\n",
    "    \n",
    "    obs = pm.Poisson('obs', mu, observed=death)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We proceed to sample from this model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [beta, lambda0]\n",
      "Sampling 2 chains: 100%|██████████| 4000/4000 [10:09<00:00,  4.35draws/s]\n",
      "There were 79 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The chain reached the maximum tree depth. Increase max_treedepth, increase target_accept or reparameterize.\n",
      "There were 101 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The chain reached the maximum tree depth. Increase max_treedepth, increase target_accept or reparameterize.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with time_varying_model:\n",
    "    time_varying_trace = pm.sample(n_samples, tune=n_tune, random_seed=SEED)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x1382.4 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.forestplot(time_varying_trace, var_names=['beta']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see from the plot of $\\beta_j$ over time below that initially $\\beta_j > 0$, indicating an elevated hazard rate due to metastization, but that this risk declines as $\\beta_j < 0$ eventually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n",
      "'c' argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with 'x' & 'y'.  Please use a 2-D array with a single row if you really want to specify the same RGB or RGBA value for all points.\n"
     ]
    },
    {
     "data": {
      "image/png": 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6/Trec889Oh6P6/Xr1+vm5mattda/+tWvMtumr1ixQj/33HNaa61vueWWfluJ9yXbaueREred/ceDzCpxU+SS+g5CTCffeeodIon+I46RRIrvPPUOV6yelfP7G24L6WzbXEN6W+2rr76aK664giuuuAKALVu28Jvf/AaAiy66iLa2Njo7O4H0NtYulytzf2+99VYmf6Gzs5P9+/ezefNmPvrRj2KxWJg5cyYXXXTRCfv+l7/8hf/6r/8C0rtpFhUVAekRkcceewyAhoYG9u/fT1lZGXa7ncsvvzzzeJ555pkh23nwwQfZvn0769atA9J7fVRWVmbO+eAHPzhkv/pu2718+fLMPh4LFy6koaGBLVu2DNn2QNkey9KlSzl48CCf+9znuOyyy9i4ceMJnyuAb3/727hcLj772c+yc+dOdu7cySWXXAKkRzGqq6vp7OwkEAhw/vnnA3DNNdfwxz/+cUTt54IEDmNkGOlEyZ1NnfzVojLZ20KIaWSoHKeTyX1avnz5kImGepgtpLNtcw3whz/8gc2bN/P444/z9a9/nV27dmXd/rr3vavvNtdaa37wgx+wadOmfuc++eSTOXmve+655/jf//1fXn75ZdxuNxdccEFm226bzZa5D4vFMmzOhdaaT3ziE/zbv/3boNucTuewm2mNZNvuodoeyWMpKSnhzTff5KmnnuKHP/whv/71r/n5z38+bFt//vOfeeSRR9i8eXPm8S1fvnzQVEsgEJjUa47kOJwEv8tGS3eMo52SKCnEdDKz2DWq4yNx0UUXEYvF+OlPf5o5tnXrVp5//vlRb09tmiYNDQ1ceOGFfPvb3yYQCBAMBvttu/3cc89RXl6O3+8f9PubNm3iRz/6EYlEeun5vn37CIVCnHfeefzqV78ilUpx9OjRfrtH3n777ZlP3X1dfPHFmZ0nU6kUXV1ddHZ2UlJSgtvtZu/evbzyyisnfH6ytXPxxRfz6KOPZp6L9vb2E24BPlLDtW2z2TLPzVCPpbW1FdM0+eAHP8jXv/71E27bXV9fz2c+8xl+/etfZ0Z+li5dSktLSyZwSCQS7Nq1i+LiYoqKitiyZQtA5jWdKBI4nKRit423GjuJJ83J7ooQYoLcumkpLlv/T7Mum4VbNy0dc5tKKR577DGeeeYZFi1axPLly7nzzjuZOXMmGzdu5O/+7u9Yv349K1as4EMf+lDWi0+vVCrFxz72MVasWMHq1av5whe+QHFxMXfeeSfbtm1j5cqV3HbbbTzwwANZf/+6665j2bJlrFmzhtNPP50bbriBZDLJlVdeyZIlS1ixYgWf/vSnM0PlkN6mesaMGYPauvvuu3n22WdZsWIFZ5xxBrt27eK9730vyWSSlStX8uUvf5mzzz77hM9PtnaWLVvGN77xDTZu3MjKlSu55JJLMsmDJ2u4tq+//vrMVNBQj6WpqYkLLriAmpoarr322szIxbXXXsuNN96YSY7sdf/999PW1saVV15JTU0Nl156KXa7nUcffZQvfvGLrFq1ipqamkxS6H/+53/y2c9+lvXr12cCjYki22r3bKt9MlqCUZZV+1lc6ctRz4QQE22022r/7vUmvvPUOxwJRJhZ7OLWTUvHJb+hUGzatImnnnpqsrshBpBttfNUicvOO8e6mVPqln0shJgmrlg9a1oHCgNJ0DB9yFRFDlgtBqaGw23hye6KEEIIMa4kcMiRYreNfce6iSakKJQQQoipSwKHHLEaBhqoaw1NdleEEGM0nXO+xNQzXn/PEjjkUJHbRm1zUEYdhChATqeTtrY2CR7ElKC1pq2tDafTmfO2JTkyh9KjDppDrSFOqx68NloIkb9mz55NY2MjLS0tk90VIXLC6XQye/bsnLcrgUOOlbgd7G8OMr/Mg8suKyyEKBQ2my2zsZAQYmgyVZFjFkNhUXCwNTjZXRFCCCFyTgKHcVDssnOgOUg4PvX2tReFI5kyae6KYpoyZy+EyB2ZqhgHhqEwDEVtc5CVs4snuztiGoonTbbVt3M0EGWG38mKOUX4naPbxVVrTVckSUswSjRhMqfETZFbdoIVYrqTwGGclLjtHGgOUeF1UH0SG98IMVrRRIpXD7bRHU0ys9hFVyTBs3ubWVbtZ0G5B6tl6IHGZMokEElwrDNKY0eYeFKjFBgqHQiXe+0sqfJR7nVgMWRHWCGmIwkcxomhFKUeO68cauPUGX6WVvkw5I1WjLNgLMkrB1tJpDRl3vRWwX6XDY9pZc/RLho6wtTMKaHUY0drTSSRIhhLEggnaOmO0R6KY2qNzWLgc1gpcvUPMkKxJK8cbMNhM1hc4aXS78RmGFgtCquhht3qt3eZo2xBL0Rhk8BhHNmtBpVeJ+8c66YzHKdmbglOm6y0EOOjM5zgpYOtGEpR7Oq/cZvFUFT4nIRiSTbva6bS56Qrmsjs6moohctuodRjxxjmwu5xWPE4rMSTJnuOdrP7SBdKgUaB1lgtBnargdVQJFOalNakTE3KNNEalAKXzYrTZuC0WXDbLbjtVnxOKyVuuwTXQhQACRzGmWEoqvxO2kMxXtjfwpnzy2SeWORcWzDGywfacNoseBxD/7P2OKy47BbC8RSeLCMKI2W3GpT3jGj00lpjakiZGk161MKh0iMMvdMdZk8gEU9qwvE4zd2aZEoDGrvNYGG5lxlFzlHnYwghJk7BBA5KqTqgG0gByYFbgqr0+OfdwKVAGLhWa71jovs5lBKPg1AsyXP7mlkzt4Q5pe7J7pIoMLFkivq2MKFYkljCJJpMEU+axJIpkqam2GUf0YiWodSwwcVYKZVeijxc7oOhFIZFke5m/74mUib7jnez52gXRS4bi8q9VBU5sVtl8ZcQ+aRgAoceF2qtW4e47X3Akp6vs4Af9fw/b3gcVuxWg211HbjslkGf2IQYSnsozra6dmKJFHabBauh0tMLPSMMw00vFAqbxaDMk/43EY4neb2hA+sRxbLqImaXuIZN6hRCTJyp9C/xr4H/0mmvAMVKqerJ7tRANouB32XlzYYAKVlfL07ANDW1x7t5YX8LFkNR7ksP47vtVpw2C1aLMSWChoHcdisVPiceu403GwM8+04zRwMRqUkhRB4opMBBA08rpbYrpa7PcvssoKHPz409x/KO224lGEtwuD082V0ReSwST/HqoTZ2Hu2izOPAbS+0AcKTZ7caVPqcWA2DVw+180JtK63B2GR3S4iCFU2kQBknlaVfSO9EG7TWR5RSlcAzSqm9WuvNfW7P9rFr0MeTnqDjeoDqWXPGp6cjUOp2sKupkxl+p+xpITJMUxNPmQTCcXYc7gAUVb7c725XaJw2C06bhWAsyZb9rZR77ZzSU09CVmIIcWJaa452Rnj9cABlc5zUm0rBBA5a6yM9/29WSj0GnAn0DRwagb6RwGzgSJZ27gPuA1i+cvWkjXtaLQZKwZ5jnayZWzpZ3RCTKBRL0todozOaIBRLEoolCcfTW7JrwO+0yfLdAbwOK16HlWAsycsH2vA4LJxS5aO62IVNciCEyCocT7KzqYumQBi7xUJ6YfTYFUTgoJTyAIbWurvn+43A1wac9jhwk1LqV6STIju11kcnuKujUuK2U98WZl6pJ1OsR0xtyZRJWyjOweYQLcEoAHarBZtFYbemaxpIgaQT6w0gookUbzQEeLupk8WVXuaUuqfllI4Q2ZimpqEjzNuNnenSAD5n5sPJySiUf2FVwGM9b6hW4L+11n9SSt0IoLX+MfAk6aWYtaSXY35ykvo6YkopfI508tf5p1RKCd8prCuaoLE9zKG2EMmUxm2zUu51SJBwknqnMJI9Szn3HutmdomLBeVeStw2eX7FtNUZSbCzsZOWYJRSjyOnI3IFEThorQ8Cq7Ic/3Gf7zXw2YnsVy54HFaau6Mcbg+zoNwz2d0R4+BoIMLWunYshsLvsmE1ZEg916wWg3KvE1NrmrtiNLRHKHLZWFLlpcrvlGkMMW3Ekilqm4PUHg/itFmo8ud+r6SCCBymulK3XRIlp6iG9jDb69spcTukkNEEMJSi2J0utx2Jp9he34HVolgzp0Q2mxNTmmlqmgIR3m4KYJqMa+KwvJPlAavFAAXvHOue7K6IHDrUGmJbfTulHgkaJoPLbqHS58Rrt/HKwXZqm7szG20JMZUEwnG21Layvb4dj91G2TivNpIRhzxR6rZzqDXIzGInlf6xr5TRWhOKpzC1Rqe3AEgfR6OUwmO3FGQFPtNMb+9cCHPWWmv2NwfZ1dRFuc8hUxOTzG41qPA5eLuxk2gixbLqIlnCKaaMxvYw2w934BqnaYlsJHDIE6pniHX74Q4uXFo5pmV4HaE4e4510dIVw1AKjU5Xt8h8yFKgNEVOGxV+B6VuB16nFafVINlTPyCRNImnTGIJE0PBjCLXhH5ajiZSBMIJwvEkoViKYCyRWaZY4razfFYRpR77iRuaJFpr9hzt4p1j3VT4nJLwmicshqLS76S2OUQ0YbJqTrHkPYiCd7wzwrb6Dko99gn9e5bAIY84bZae9badnDGvZMSfrjsjCfYd76apI4LLZhl2xEJrTSxpcqglTK0Z5N3IIn1f6f/q9DbJaCxNnSyd4WNuqWfcA4hgLMkrB1oJxVMYSmGzGP2WKYZiKTbva6a6yMVpM/15tYOi1pquSJKDrUHq20JU+p1TshR0ITOUotLn4GhnlEi8jXULSqVOhihYrcEYrx5qp8Q9sUEDSOCQd0rcdhraw1T5nSfcQbM7mmB/czcNbZGe0rwnXt6nlMosYRuJRMpkd88n6PEMIALhOC8daMVipEsMZ+N1WvE4LLSH4jy7t5n5ZR6WVHkz6/Z7t3VOmiamCQ6rMe5D0tFEiuOdUWpbggRjSWwWgwqfBA35SilFuddBRzjOlv0t1MwtocxjL4gpMCF6dYTivHygDZ/TNin5UxI45BmlFKUeB282BCj12LNuf6y15lBriJ1NnVgt6fnb8Xrjs1kMKrzOfgHEvDIPTpuBw2pgtRhYDIXVMHDbRx6Q9NXcFeXVQ+247ZYTFu/pndIxtaaxI0x9Wwi33UrCTE+z9A6gaNJZxavnFo9LQaDWYIwDLUGOd0ZRSuF1WIcMeET+KXHbCfWUr67wOji12kepBBCiAHRGErx0oHXM77e5IIFDHrJb0xfjNxoCrF9Y1u9TczSR4q3GTo4EwpR5Jy7xrjeASKZMGtrDpEyNqfW7O4RocDusnLukHId15H/Mje1httV3UOQaXXlloyfAMk1NSmucyoLh7J882RmJ8+yeZtbMy+1SvIa2MNsPt+O2SxGnQuZxWPE4rHRHE7xQ20qlz8GpM/x5nUMjprd0qfXWzPTtZJHAIU8Vu+0c745yqDXIokofAG3BGFvr20ml9IRlzw5ktRiZdfIDtQVjvN04svwMrTUHW4K81dRJ2UlUNTMMhZF1fzMoctmJJ01eOdjOwgoPp1X7T3pY71BriDcaOij3OApydYoYzOe04XPa6Iom2LyvmRlFLk6fVYQ3y2ifEJOlK5rg1YNtmRHOySTvfHmszGNn15EuOkJx9h3v5oX9LdgNC6We/NzXotRjp7EjQl3b8NuFa63Ze6ybt5o6KffmthTqQHarQZXfQUN7mM37m+kIxcfUjtaa2uPdvNkQoNwrQcNU5HfaqPQ56QjFeW5vM0cCsu29yA+N7WGef6cFtMqLpHB598tjVsPAZbPywv4Wdh/potyb35UllVKUee281RAY8gJtmpq3mzrZe7SLSq9zQqZa0v1ygFZs3tdCU8foLgi9gc7bR9KBjtRlmLp6c2h8ThuvHergrcYAiZQ52d0S01QyZfJ2Y4Bt9R34nTa8zvwYBZN3wDzndVrxu2xU+QujJoDVMPA6rWytayea6L8LW8rUvNkY4EBLz3LFCX48HoeVEo+drXUdNHdFR/Q7pqnZdaSTvce6qfQWxmsgTl5v0aj6tjAv7m+lK5qY7C6JaSYcT28df6g1RIUvv6rP5kf4IoY1mmTDfOC2W2kPxXizMcC6eaUYhiKRMnn9cICjnRGqxnEVyInYLAZFLhuvHGzjvFMqhszXgJ6lqEe6ONgapFKWWE47Rs/Sze5oguf2NrN6bgmzS1ySDCtyoiuaYN+xbgxD4bZZ8DgsOKwWbBaDWDKjb+V1AAAgAElEQVS9z4rFUFTk4WotCRzEuCj1ODgSiHDQE2ROqZttdR20h+J5sWTRabNgas2Lta2cd0oFvixzhp2RBNvr2wnFUlT5nHKxmMZ8zvSKn+31HdQ2B1k6w0uV3yWjT2JMtNYcbg/zZkMAW89y9kRKkzJNQKEUmFrjd45updlEksBBjJsKr5OdTV00tEcIx5OUe/MnqdNtt5IyNa8cbOOcxRWZ3BGtNQ3tYd5oCOCyWfOqz2Ly2CwGVX4n4XiSrXUdOG1dLK3yMbN4Ykuyi8L27nL6CGUee8EmWUvgIMaNxVAUuWzEkmZergTxOW10RuK8erCN9YvLUCjebgpwuC1dI0P2MhADue1W3HYr8aTJW40Bdh3pZEmVj4XlnoK9CIiJ0dIdY3t9O6apR1TlN59J4CDG1WjKW0+GIped9lCMrXUdRONJIokUVX6ZmhDDSydPpgui7TnaRXNXjLXzS/L6b11MjmgixYGWIPuOBSl25+/0w2hI4CCmvVKPg/ZQDIfVQrl38nMwROGwWtJ7q3SE42ypbeGsBWVZc2bE9BNLpqhvC7P/WDcaqPQ5psx27hI4CAF5OZUiCkeJ2053NMHmfS2cvbAsXTdETEuxZIqGtjDvHO/G1FDstk252i8SOAghRA74nDaiiRRb9rdyxrwSZp9gd1sxtaRMTV1rkL3HegIGl23K5r1I4CCEEDnitFmwGIqtde2EEymWVHolX2YaCMaSvHE4QFsoSql76pekl8BBCCFyyNaT97DrSCcum4U5MvIwZWmtaeqI8EZDoCffZXI2H5xoEjgIIUSOGYaizOPgjYYARW5bXmxMJHIrlkyx+0gXdW0hSt35VRJ6vE2fRyqEEBPIZjGwWw121HeQlI2y8loiZWKaekTnmqamNRhj874WGjvCVPmc0ypoABlxEEKIceN32mjpjrLnaBcrZhdPdndEFp3hBC8faiVlwswiJ9VFrkH1FhIpk0A4wbHOCI0dEWJJE5/TOm2Xb0vgIIQQ46jM66C2OUiFz8GMoukxB14oWrqjvHKwHbfdgsducLwrxuH2MJBeYjuzyEl7OM7xrhim1tgsBj6HlWL39BphGEgCByGEGEeGUpR47Gyv7+DCU2247fK2mw+aOsJsq+vA73p3dKHIZQA2tNZEEyZ7jnXjsBqUeuyyO24f0ztsEkKICeCwppdpvn44QGqEc+li/BxqDfHaoQ6K3fasJaCVUrjsFsq9DnxOmwQNA0jgIIQQE6DIZac1GKO2uXuyuzJtaa3Zc7SLNw4HKPfZp11SY67ImFkfrzY/w2P1P6M91kypo5Ir513HWZWXDHlcCCFGo8zjYPfRLkrcdir90zOxbrIkUya7jnRxsCVIpc85ZfaNmAwFETgopeYA/wXMAEzgPq313QPOuQD4PXCo59BvtdZfG+l9vNr8DA/W3kXcjAHQHjvOg7V3Udu1k5eb/zToOCDBgxBiVCyGothlZ2tdOxcsrcTjGNtb8LHOCG83dbKk0sfsEteUr1R4skKxJNvrOwhE4rL7bQ4UROAAJIH/T2u9QynlA7YrpZ7RWu8ecN4LWuvLR9poUyDCfzyzD6tFcdR3LylLrN/tcTPG80f/B5Q56Phj9T8DkJEIIcSoOG0WYkmTbXXt/NXicmyjvOjXtYZ4vaEDn8PGm40B9h3vZvlMP9VFrqyfomPJFJ3hBN2xJD6HFY/DittumTYXz+auKFvr2rEYBhXTdPlkrhVE4KC1Pgoc7fm+Wym1B5gFDAwcxixldAxxS/bCLb0jDzISIYQYrSKXjdZgjN1Hulg5u2hEF3GtNe8c62bP0W7KfQ6shoHHYSWaSLG1rp0il53ls/xUeB2E4inagzEaOyK0BmNo0qs7tNagwGIYlLhslPsc+JxWLIbCUAqLSv/fMMBuNXBYBycOFgrT1NS2BNl1pJNiV/YkSDE2BRE49KWUmg+sBl7NcvN6pdSbwBHgFq31ruHamlXs4p8uOYVit53btlbRHjs+6BxDGZjZggdtZIKGXr0jERI4CCFOpMxj52BLkCKXjfnlnmHPTZmanU2dHGodPD/vtFlw2lyE40leqm3DblUkU+nb3D0rAwYGJqapiSRS7DvWjdYarQCtSP9Pk/4O5pS6mFvqocRtK6gRilgyxZsNnTQFwlR4nVgknyGnCipwUEp5gd8AN2utuwbcvAOYp7UOKqUuBX4HLMnSxvXA9QDVs+Zkjl8577p+IwgAdsPB+sr39stxAFDahiaRtY/tsWZJphRCnJBSinKvgzcbAvhdNko99qznJVImOw53cKwzSqVv6Pl5t92K224laZpYjeGnPwxDZc4fimlqjgai1LeF8TisLKnwUlXkzPtP7p3hBFvr2oglTaqGeb7E2CmtC2NNsVLKBjwBPKW1/o8RnF8HrNVatw51zvKVq/VdDz1JsTv9D3Y0qyrSPw8eofBY/CR0bFAAcs3iWyR4EEIMEo4nSaRMzj+lEpfdQsrUhONJIvEUXdEEje0RgrEkZV7HpPUxmkjRHUsAinmlbuaXeyhy5dfGXVprDreHeaMhgMduHXPi6VQXiiXZuHrhO2YsdOpY2yiIZ1alQ8b/C+wZKmhQSs0AjmuttVLqTNI1KtpGcz9nVV6S9eI+1PGBIxRK24gkUpiGTGEIIUbGbbcSiMR58UArhlIEo0lQ6Q90BgqnzTKpQQP0TodYMLWmKRChri1Epc/JkiovZR77pH+qT6RMdjZ1UtcaotzrkFUm46wgAgdgA3AN8LZS6o2eY18C5gJorX8MfAj4tFIqCUSAq/Q4Dqf0BgG/rP0J4VQrFrMEf/QDdLgfyHp+e6x5vLoihChwxS474XgSQ0G5d/IvxEMxlKLEbUdrTVc0wYu1rfidNpbO8FLld01KLkFXNMG2unZCsZQstZwgBRE4aK23AMP+NWit7wHumZgepWUbibht65+yTmGUOiol90EIMaRC2sNCKYXfacPvtBGOJ3mtrgOnrZPFFV5ml7gnLA+iqSPMjsMBHFaD8kkelZlOZDwnx66cdx12o/8fsN1wsKLkbB6svasnqNCZ5ZuvNj8zOR0VQogccNutVPmcuKxW9hzt5undx3mzIUAgHB+3+9Ras/94N6/VteN32vA58yvfYqornBC3QPSOINy/516SRgdWswRP6ANsSTyetcDUROQ+SCltIcR4s/d86jfNdB7EodYQZR47p88qomSIFSNj8e7S1JAstZwkEjiMg7MqLyHYtpIXD7y7oGOych+klLYQYiIZRjoPAiAYS/JibSvnLqmgyH3yowKxZIod9R20dMeo9A2uTyEmhgQO4+Ti06q4+LSqzM9DFZgqdVTm9H7/vOd4v4BlLKW0JXAQuTbU6NaW2hYe3tpAazBOudfOR9bNweZ/Q0bCpgivw4oCXj6YDh5OZolkMJbktUNtROIpKnxSOnoySeAwQYYqMHXlvOtyej8vHmilvi3MvDI3MIZS2tHjfO2JdMHNDYvK+wU/D9V+lxeO/Q8mJgYG5854P1cv/kJO+y+mnqFGvfY2WPnLWx7iyfTfYmswzk821+KY8RSG/3i/c0FGwgqVx2GlK5LglYNtbFhcPqbEyY5QnJcPtmJRBqUeSYKcbBI4TJC+uQ8po4NSZ9WYP0k9VPtdNh/7H7Q2AQN3bAOl0asAMkHDHZcvB4Ye6RiqlLbFLMm0A62ZwOGh2u/y/LHfZ84zMTM/S/Agem2pbeGBl+oIxlJYDUWlz064Kvuo11NvxdFJV7/jyZQidfxivP5t/c6VkbDC5nfZ6AjF2FbXwVkLS0e1sVdbMMZLB9pw2y0FtfJkKpNVFRPorMpLqO7+BrM7f8i31j085qDh+WO/R2OmF6gqk7DjBdqdvwJgXpmbDYvKM+cPtcrj3Bnvz3r82tM+wx2XL2demZv6tjBfe2IXX3tiV3pqI4sXjmU/LqafLbUt/PSFQwRj6Y0SkqbmaGeMSPe8rOfrpH+I48WDjkkdlMJX4nHQHorzxuEApjmyEjttwRgv1rbiOUF5bDGx5JWYBL0X5IEGTg3A4JyFxqL/GVzRQkHU+SJ3vOfrg9rsDU6yzRkv9p8+5FxyOvjoW607+9RG1g3AJoCsCJlc2UYWmrvjJAdcEDSQbL0Ue/Ebg9qw2LpJJQYHD8oaGHQs17lAYnKUe+0c6QzjOGKwYtbwu4K2dEd5+UAbPqct7/fHmG4kcJhggy/IaQOnBnoNzFkYywV8tKW0YXBy541bsk9tGJMwaDXUnDnIPHiuZUteBPjpC4cyuQm9IwtDfYZMJXzYDceg/J4NK2z85S0j0w6A1aJxVP253++PRy6QmBzpjb2cHGgJEYmnWFDhoczjGLSksrkryssH2/BL0JCXJHCYYAMvyL2yjUD06puzMFkX8HNnvL9fjkPf47k0cIQlm6FWijxW/zMg++iKGL3eqYe+yYv3PnsAQ0FqQJSgAUNBthHocq+Djy2+JcvrciGLitKBSVswTllmVcUm7t9zoF8dlKdem8lTZE/aFYXFUIpKn4NAOMHLB9qwWwzml3uYVeLC77TR3BXllYNtFLlsOKwSNOQjCRzy2KvNz6QvkkYHt21NJ1NO1AV8oN4EyHSug4mhxr6q4tXmZwbt8eFJnAnAnqPdAJxW7Rvy94daKdI78iAjEWMzMGjbfzyYdephYNDQy9TpIkB9RxDsVoOPrJvDWZVrsr4G5yyu4JzFFQOODq6D0muokTlRWAyl8Lts+LGRTJkcaAmy73g3RU4bnZEERW4JGvKZBA55qnc4vveTde9F8JrFtwBMyrLIqxd/gQN7N1LfFmZ2mZsDAfja3ndHSkbySbDfNIOClKWDgPu/IQyexJmcVu07YTtDrRRBG/2Gw0Ey8kdj4LTYwKDhRHqnMgaOIAwODE5sLCNzojBZLQZlPUssI/EUJR77qFZdiIkngUMe6Zs0Odxw/LfWPTxpSyBHm6MxkoJUWiVQpX/ijnWfHFEfstXEUNqGJpH1fMnI72+o6aCBS3k/98sdtAYH7zfgdViIp3TWkYXsIwi5NZrkYlFYXHYZZSgEEjjkiYEX5KGH4yf3IjjaT4IjLUg1msc11EqR9M/jX50z34wkL6SvoaaDBi7l/ci6Of1yHCAdIHzir+YD5GRkYbRGG7gKIXJPAoc8MVklqsdTb46GpaiDcE/Bq8fqc/O4hloRkqvqnKNd7plt9cFEXEgh28qb4Y1kOgjI9H+oAGGiHl9fMoUhxOSTwCFPTVSJ6vEyVI7G+sr39ttcC3L3uIbamXS0GfmjXe6ZbfXBT184BOT24jrSKYZcmoiph1yRKQwhJoYEDnlquMJN+WokORpvd7zCNVmX5uXmcWXbmbRv/8aahxE3Y9y/516eem3moHazrT6IJ01+8vxB/rI3d1NLI51imI5kCkOIiSOBQx4brkBTvhlNjsZ4P67RDGe/2vwMjzbfS7IoPULhj35gyL4PdXyo1QejXZVwIiOdYpiOhnvNZSRCiNySwEHkRCHmaPSdTlGkl4aGfL/CY/gJJbsGnV/qrOKOcwdPBwy1+qDcax+X6QMxcjISIUTuSeAgxkW+5miMZDrFphxZSyQP1fehVh/0lmcWk0eSKYXIPQkcxLjIxxyNkU6nhFLd/MMpXxpx30+0+kDkJ5nCEGJsJHAQ4ybfcjRGM50y2r4X0uoDIVMYQpwMCRzEtJWv0yli/EkypRBjJ4GDmLbycTpFTC4ZiRDixJTWuV0yVkiWr1yt73roSYrd9snuihAij/WORGSrzjlwJGK0VUeFmEihWJKNqxe+Y8ZCp461DRlxEEKIExjpSMRoq44KUYgkcBBCiBMYaU7EcLvaSuAgpgoJHIQQYowKZVdbIXJJAgchhBijQqyYKsTJMia7A0IIMVVcOe867Iaj3zFZ4iummoIJHJRS71VKvaOUqlVK3ZbldodS6uGe219VSs2f+F4KIaazsyov4ZrFt2BJlYCGUkcV1yy+RfIbxJRSEFMVSikL8EPgEqAR2KqUelxrvbvPaf8AdGitFyulrgL+D/CRie+tEGI6O6vyksz269k2RROi0BXKiMOZQK3W+qDWOg78CvjrAef8NfBAz/ePAhcrpdQE9lEIIYSY8gpixAGYBTT0+bkROGuoc7TWSaVUJ1BGtsXXQggxwbbUtvDw1gZag3HKZSM0UcAKJXDINnIwsOTlSM5BKXU9cD1A9SzZ9lgIMf621Lb023q9NRjnpy8cApDgQRScQgkcGoG+V/nZwJEhzmlUSlmBIqB9YENa6/uA+yBdcnpceiuEmPb6FobafzxI0uz/dhNPmjy8tUECB1FwCiXHYSuwRCm1QCllB64CHh9wzuPAJ3q+/xDwFz2dN+IQQkyaDYvK++1rMTBo6NUWjE9Ul4TImYIYcejJWbgJeAqwAD/XWu9SSn0N2Ka1fhz4v8CDSqla0iMNV01ej4UQ09nAwlCf++UOWrMECWVe2WBPFJ6CCBwAtNZPAk8OOHZHn++jwIcnul8AsWQK0wSlwFAKpd793pCFHUJMex9ZN6dfjgOA3WrwkXWSZyUKT8EEDvlGa013NEk0mcLjsOKyWUiZJilTk0ppUloTT5porSn1OLAYEkAIMV315jH85PmDJE0tqypEQZPAYZSSpklnJEEqpakudrKoooRSj51sJSOSKZODrSH2Hu3CYbXgd9kmocdCiHxwzuIK/rI3vdnVHZdLYShRuCRwGCHT1LSHYhiGYmGFh7mlHryO4Z8+q8XglCofM4qcvN3QyfGuCCVuB3ZrfuSkRhMpuqIJIJ0l63fZ86ZvQggh8pMEDiMQiiUJxZMsrfKxsMI76our32lj/aIymjoivNUUgBiUuLOPUoyUqTWdkQRFThvGKKZBtNYEY0kiifQUy5o5JRR7bBzvinKgJUQgEsdhteBzWjP5GSlTE02kiCZSmFpjKEWZ13GCexJCCDEVSeAwDNPUtIVieBxWzj+lgmL32DOgDUMxp8xNhd/BzqZOGjrCVHqdo7ro99Ja0xqMUu510BqM4bZZ8TqHfylNUxOIJEiaJhVeB6vnllDmsWfu3+e0sbDcS3s4Tl1biCMdkczvWi0GpW4788vc+F02DrWFaO2OUeqR4EEIIaYbCRyGEI4n6Y4mOKXKzylVXqyW3AzhO20W1swtweOw8s6xbko9dmyjbLstFGdWsZs1c0vojiZ5vaGD5u4opR47VqN/W4mUSVckgak188o8zC/3UDREroVhKMq9Dsq9DqIzUwRjSTx2K06b0W90xO+ysXlfC+F4Erdd/oSEGI2+haH62rCovN8STiHylbzrZ9ERimO3Kc47pZJST+7XWRuG4rRqP16HlR31HficNlx2y8j6Fo5T4razak4xhqEocts4d0kFda1Bdh3pwmYxKHbbicRTdMcS2CwGp87wMbvUjdM2svuAdIAz1PlOm4UzF5SyeV8LdouRs6BKiKluw6Jysm2fU98WBlolcBAFQQKHAeJJE8OA85ZUjnui4JxSN267hVcOtpEwTfzO4VdddEUSOKwGa+eX9BulsBiKRZU+qopcvN0Y4HhXlCKXjbXzSqjyO8flwl7strNydjGvH+6gyu88qXwNIaaLgYWhemUbgRAiX0ngMEAgEmf1nOIJW11Q5nVw/tJKXjvURlswRrHbnrXmQziexERz9sLyIUcCvA4rZy8sozuWxOewjvvFfF6Zm45wnMaOCOWTkCyZnk5K8u7TpUDp9NZmSmFRalxGjIQYDzKFIQqFBA59RBMp3HYLs0rcJz45h7wOKxsWl7PnSDdNnRFSqXR1OYfNgttuIZnShOMpzltSgecES0CVUiccucgVpRSnzyoiEI7TFU2M6n6jiRTAqKZPeiVNk45QHLfDwobF5ZR77fTuSqJJJ48mTc3WQ+10hGKUSBKnyHMyhSEKiQQOfXRG4py5oHRSqjw6rBZq5haz0iwiGE/SGU7Q3B3jeFeUlKk5a0EpRe78KyBlsxisnV/Kc++0EE+aw47UmFrTFUkQT5l4HBZSZnqpa4nHPuLS3IFwnETK5LRqPwvKPZlpmP6/rrBaYN2CUl460EpnJE6RS0YeRP6SKQxRSCRw6BGOJyly2Znhd01qPwwjPWLgd9qYU+pGa008ZeKwjv6T+UTxOW2sm1/C1roONOmP/gYKh82C02aQMjVdkSSgmVXiYn6Zh1KPnXjKZO/Rbg62BCl224ccfdBaE+kpVlVd5OL0WUUnLL4F6dGMsxeW8WJtK93RBL4JGokRIpdkCkPkGwkcenRHE/zVovIx1VUYT0qpvA4aes0ocnHpCifheJJIPEVXJEFrKE4gHMeiFCtmF1Fd5OwXHDisFlbNKaa6yMmOwx2EYsl+5bsj8fSSUNAUu+2sX1g26kRMtz2d9/HC/hZCseQJp3qEyCcyhSHykbyLAsFokjKvgwqfzIWfDIuh8Dlt+Jw2Kv1OFvcc11oPe7Gv9Du58NRK9hzppq4thMVQmFpT5LKxanYRFX7HSdWL8DltbFhUwQv7W7AYakx5FWJimVoTjCaxW41p/XrJFIbIRxI4AKF4gjXzKmRJ4TgZyfPam+NRXeQgnDCp9DlyOjpQ5E6X/d5S20o4nsJhNbBbjVEX3xIn50RBZCJl0hmJY2qoLnJxrDOC1VBSK0SIPDLtA4fuaJK5ZW7ZeyFPVBWNX45JmdfBeUsqONYVoTOSrgwaiMTTN2qwGAZ+p1UuUuOgd+msxVA9K2B0zzRcekQhnjQJxZPYLQanzvAzq8SF226lrjUktUKGILkPYrJM+8BBozlthn+yuyEmSInHTkmf2g7JlEk0aRKOJ2npitHQESaWNLEYCq/DWhD5Jfls4NLZMo+dSCJFKJ4kGE3S3pMH47RZWD6zlAqfo1/g1lsrpKkjIsF9H6PJfdhS28LDWxtoDcYp99r5yLo5nLO4YuI6K6ac6R04KFhS5c3LZY5iYlgtBl6LgddhpdLn5LRqP13R9FLYw+0hAl0JfE6r7MkxSlprOqMJEkmTZdV+5vdZOutxWPE4rFT6YOEJrl9KKZbPLKIjHJeVMX2MNPdhS20LP33hEPFkujZMazDOT184BCDBgxizaf1uaOsZFhWil2Eoit12it12llR6aQvFebG2FathTFg10UIXTaQIhBPMKnGxbKZ/REtnh2O39tQK2duMw2qR1+EE+k5h7D8eJGnqfrfHkyYPb22QwEGM2bT+F2g1lHySFENSKr1b6BlzS2gLxUgNeAMWg3WE40QSSdYvKmXd/JKTDhp6+Z021swtoT0Ux9TyOgxlw6Jy5pW9W/l2YNDQqy0Yn6guiSlIrppCnMDsUjfhRIpdTZ2SpDeEpGnSGoxR7Xeyak7JiHd7HY3ZpW7aw3HqW0OU+5w5b38qGDiF8blf7qA1S5BQ5pVKqmLspvWIgxAjtaTSy/xyD63B2GR3Je+EYknag3FWzCrizAVl4xI09FpW7afIbX93NYwY1kfWzRk0taMAu0XxtSd28bUndvHnPccnp3OiYEngIMQIKKVYMauIUq+DjrBctCCdANkWjIHSnL+0gsWVvnGvvGq1GKybX4rDasjrMALnLK7gU+cuwOtIB3NWQ1Fd5KDInR5xqG8L8+KBwaszhBiOTFUIMUJWi8HaeSVs2d8y7TP8tdY0d8eYV+Zm+cyiCU1YdNkt/NWicl471E57KEap7H46rHMWVwyZCCkVKMVYSOAgxCg4bRbOXFjGC++0EE2kpm055NZgjDmlLlbNLp6U/V2cNgtnLSxl66EO2oIxqfFwEqSQlBgtmaoQYpT8ThtnLyqjO5rIrI+fTtqCMSr9zkkLGno5rOngodxrpyUYRctqi1EbuAqjl0xhiOGMesRBKfVVwAZsB7Zpretz3ish8lyZ18G6+aW8cqiNco9j2pSpbg/FKHbbOWNeSV48ZpslXePhjYYATYEIFV6HrHoZBdlES4zFqAMHrfVXlFIVwDrgWqXUAmC/1vr/z3nvhMhj1cUuVs8p4Y2GABVeR95tyZ5rnZE4HoeVdQtK8mpzMKvFYPXcEqyGweH2EJAuFz6eqzumA5nCEEM5YeCglLoOuAL4DfBL4J8AC/A7rfWTPed8Zjw7KUS+ml/uIZ4y2XWki0qfA2OKftrtiiawGoqzFpTl5f4dFkNRM7eYU2Z4aemKcagtRHN3FAPwOm3TNhdlrEazF4aYfkYy4nAL8CHgJtJBw3bgJeAHSqn/1Fo/oLW+dxz7KEReW1LpJZpIcbAlRKVvag2Va60JRBIYBpy9qCLvP8W77VbmlVuZV+4hGEvS3BWlri0sQcQoyRSGGM5IAoe41nqnUupm0iHoWq11TCn1APAC8MB4dlAp9R3g/UAcOAB8UmsdyHJeHdANpICk1nrtePZLiF5KKU6fWUQiZdLUEaFiilQ1DMaShGJJ5pS6OK3aX3Dl2b0OK94KLwsrvHRHE7R0x6jvDSKUwmOX6YyxkCkMMZJ3gseUUr8H7gc+o7XuLZ2XAMrHq2N9PAPcrrVOKqX+D3A78MUhzr1Qay2pwGLCGYZi1exiEinN8a4I5R5nweY8xJMmHeF0EuS5S8qnxFJHn9OGz2ljYYWXYCzZE0SEON4VxW41KHLZpuw0Uy7JFIaAEQQOPcmQG4EPAGcopb4B7AccQIdS6jTgHa31uKxL01o/3efHV0hPmwiRd3qrGr5zrJt3jnVR6nEU1E6Opta0h+JYLYoz5pUyq9hVsMHPcLwOK16HlfllbjojCerbwtS3h1Gkl9rm6jXTWk+paSuQKQyRNqKxx56L99MAKv0vYSmwGqgB7u75ed449bGvvwceHqqbwNNKKQ38RGt9X7aTlFLXA9cDzJ07d1w6KaYvi6FYNtNPidvGtvoOHFajICpM9m5StaTSyylV/oIKeMZKqXe3UF86w0djR5jaliAd4RRuezq4GO2FX2tNMJYkkkiRSmmK3LaCm+IZK5nCmD7GshxTA3t7vn6Zi04opf4XmJHlpn/RWv++55x/AcmCy0oAACAASURBVJLAQ0M0s0FrfUQpVQk8o5Taq7XenKX/9wH3Aaxdu1YqxohxUV3s4nynla2H2mkLxSh12/P202c8adIeilMzt4T5Ze687ed4ctosLK70saDcS2swRl1biOOdUQA8Disum2XY5yWaSNEdTQI6XRxrTjEAL9W2nvB3pwKZwphe8iIU1lq/Z7jblVKfAC4HLtZDlIfTWh/p+X+zUuox4ExgUOAgxETxO22cu6SCt5sCHG4L4+5JxsunGgjpC16CsxeWUl3smuzuTDqLoajyO6nyO4kmUukgojXUsytq78Vfo3t/6jnksVtZObuIKr+zX8Ll3DI3xzqjU34/DZnCmF7yInAYjlLqvaSTIc/XWoeHOMcDGFrr7p7vNwJfm8BuCpGV3WqwZm4J1UVOjnfFaOmOEejZ1VEphdtumbSh7GAsSSyRYsPiqZEAmWtOm4XZJW5ml7gJx5O0BWNonc5lsRoKi6GwGgZWS/p1zDaqsKy6iKOBKImUmVcB40SSKYypJ+8DB+Ae0omYz/T8w3xFa32jUmom8DOt9aVAFenVH5B+TP+ttf7TZHVYiL6UUswsdjOzOL0nQDSRIhhLEgjHaQpEae6OUu7NffEorTXheAqlwFCq5yv9fXcsgVKKc/9fe/ceHtdd33n8/Z27RqO7ZFm+xZItO7bTkATZJMQJgYQAWSDcWsKyLWy7Db3AFvrstrD06aa7z9OHa2mX7ZaGFkp5WAhQLlkIJIWWBCiBOMGJHWwnxkmwY8eWfNN1ZjTSb/84R2Esz+gunTMzn9fzzKOZM2eOvr8ZjeYzv/M757elg6a68I/BCFo6ESPdOv9/l3WJKJetbWLv0XN0NlbHYbrzsVy7MH5wuJ+7HjrKwHCe9kyCN+9cX3YGUFl6oQ8OzrnNZZYfB27xrx8BXrCSdYksVCoeJRWP0p5J0t2e4eBzgzzx3NCSHoWRHZ/g/Ng47ZkE0YgxPjFJYdKRn5hkfMKRSUbp29haMwP3grS+Nc3Tp0cYzhXIJGvr+V6OXRg/ONzPJ7//1PMTzA0M5/nk958CUHhYIbX1VywSMtGIsWNNEy3pOA8/c27RR2E4/5DKaNS4uqeV1U0atxC0qH+Oj/ufOEU6EdX5InyldmGU2n3x3QMnL5ip88mTwxQmLxzqli9MctdDRxUcVoiCg0gIrGlOk0nFF3UUxlQvwyVtabZ1NerUyiHSUp+gpyPDM6dHaM/U3i6L6UrtwjhwYogDJ4Yums77wIkhALZ1NQBcFBqmDAznnw8iGj+xvBQcREJi+lEYUX/gXaxoEF40YjgHE5OOSedfJiFbKBCPRrimp5VO9TKE0pZO71wR+cJkTZwnYyaldmFM71mYsq2r4YIg8K7PP8LAcP6i9WL+ycrKBZCZKGjMj5U5urEm9PX1uT179gRdhsgFnHP0D+XIjk8wki8wmp9kLO+dVChXmHw+SMSjRiIWIRaNUJ+M0tOeUS9DyB07M8qeZ87W5EDJpTJ9jAN4Ry/99nXd7N7cUTaAlDO9R2MuFhs05ju4cykHg47kCtx8Zc+hydzIpQutXz0OIiFjZqzSB0tVWttSx7Gzo5wZzdOSTgRdTkWa+sC866GjnB7O0zbtg7TcgMxyFhI0FtOjMd/BnQsZDLrcR52ox0E9DiKygrLjE3zv0CkS0ahm56xAi+3RKDW4E7xdLb2dmYuWz2X9mYIJXNgjox4HEZEKk4pH2bmxle8/OUA85u12ksqx2B6NcoM7F7p8eg9IuaNO/vb+I/zLwVNMlNnefCg4iIissLZMksvWNrL/2fOsakhV/VwWtWx60Cg3uLM9k+BPX73jouWzrb/YYLIQiroiIgHoac+wpjnN2dGLPxSker155/qLjqpJxCK8eef6Ba1/47ZO/vTVO56/tGdKj52ZChp/9IoF76F4noKDiEgAIhHjBeubSMQijOQKQZcjK2T35g5++7pu2jMJDO8DfWr8wVKsP99gshDaVSEiEpBkzBvv8MAT/ST9Q2ul+u3e3DGvoxzms/5sR50sBQUHEZEANacTXL6umZ8ePcdqHYYrS2C+wWS+FG9FRAJ2SVuazoYkQ9nxoEsRmZWCg4hIwMyMrasbGM1PBF2KyKwUHEREQqC1PkFbfYJhDZSUkFNwEBEJATPj0q5GHWEhoafgICISEu2ZBC31CYUHCTUFBxGRkDAztq1u0O4KCTUFBxGREGnPJGmqizOaV3iQcFJwEBEJkUjE2NbVwJB6HSSkFBxEREJmVUOKTDLGmA7PlBBScBARCZlIxNje1cBgVhNgSfgoOIiIhFBnYx2ZZIzsuHodJFwUHEREQiga8c7rcH5Mp6GWcFFwEBEJqa6mOjLJqMY6SKgoOIiIhFQ0Yly+vpnB7DjOuaDLEQEUHEREQq0jk2RtSx3nNXOmhISCg4hIiJkZ27saGS9MUpicDLocEQUHEZGwq0/G2NbVyNkRHZ4pwQt9cDCzO8zsWTPb619uKbPeK83skJkdNrP3rnSdIiLLqbu9nnRCAyUleKEPDr6POeeu8C/3TL/TzKLAXwOvArYDbzGz7StdpIjIcolFIxooKaFQKcFhNruAw865I865PPAF4NaAaxIRWVIdmSRrmjVQUoJVKcHhnWb2mJl9ysxaSty/FjhadPuYv0xEpGqYGdvXaKCkBCsUwcHMvmNm+0tcbgX+BtgEXAGcAD5aahMllpXsyzOz281sj5nt6e/vX7I2iIishIw/UPLMSF67LCQQsaALAHDO3TSX9czsk8A3Stx1DFhfdHsdcLzM77oTuBOgr69P7zoRqTjd7fWcHR3n+Lkx0okoDal40CVJDQlFj8NMzKyr6Obrgf0lVnsI6DWzbjNLALcBd69EfSIiKy0WjbCru5Xrt3RQn4hxcjDLSK4QdFlSI0IfHIAPmdk+M3sMeCnwHgAzW2Nm9wA45wrAO4F7gQPAF51zjwdVsIjISmitT/DizW1cu7mdWMQ4OZjVbJqy7EKxq2ImzrlfL7P8OHBL0e17gIsO1RQRqWZmRkdDkuu3dHByMMsjvzjLpHOkE6H/9y4VqhJ6HEREZBaRiNHVXMe1m9sZzU+QK6jnQZaHgoOISBVpTid4UXcr50bHKUzokE1ZegoOIiJVZlVjihduaGFgOMfkpA4ek6Wl4CAiUoXWt6XZvqaRU0NZne9BlpSCg4hIldrS2UBPR4b+4VzQpUgVUXAQEalSZsZla5tY3ZRiQOFBloiCg4hIFYtGjCvXt9DRkOTkYFZjHmTRFBxERKpcIhZh18ZWtq5u4NRQlnxBR1vIwik4iIjUgEjE2NbVyIt6Wjk/lmdYp6iWBVJwEBGpIWua07xk6yoMx9kRjXuQ+VNwEBGpMU11cXb3dtBan6B/KBt0OVJhFBxERGpQKh5lZ3cbnU0pTuuIC5kHBQcRkRoVjRhXrG8mnYwymB0PuhypEAoOIiI1LBmLsnNjK4XCpKbkljlRcBARqXENqTg7u1s5N5anMKlDNWVmCg4iIsKqxhRXrG9hYCinuS1kRgoOIiICwMa2ND0dGZ2eWmak4CAiIoA3t8WONY20ZZKcHc0HXY6ElIKDiIg8LxaN8MJLWkgnopwZUXiQiyk4iIjIBVLxKC/e1E5bJsGpoazGPMgFFBxEROQiiViEnRtb2dhWr1k15QIKDiIiUlI0Yly+rokda5s4NZRlfEKHaoqCg4iIzMDM2NLZQN/GVs6O5nWSKCEWdAEiIhJ+61vTJGMRHjxyGuegLhENuiQJiHocRERkTlY1ptjd28FovsBovhB0ORIQBQcREZmz1voE125uJ5ufUHioUQoOIiIyLy31CXb3dpAdn2A4p/BQaxQcRERk3prScXb3djA+McFwVuGhlig4iIjIgjTVxbmut4MJN8m50bxOFFUjFBxERGTBGlJez0NLfYJTQzkGx8YVIKpc6A/HNLO7gK3+zWbgnHPuihLrPQ0MARNAwTnXt2JFiojUsEwyxtU9bZwdyfPEySFOnM+SikdpTMUws6DLkyUW+uDgnHvz1HUz+yhwfobVX+qcG1j+qkREZLqW+gQv6mnj3GieQ895ASKdiNKQigddmiyhitlVYV5s/TXg80HXIiIi5TWnvQBxw9YOEtEIA8M5JrX7ompUTHAArgNOOueeLHO/A+4zs4fN7PYVrEtEREpoTie4tredDa1pTg3myBc010U1CMWuCjP7DrC6xF3vd8593b/+FmbubbjWOXfczFYB/2xmB51zD5T4XbcDtwNs2LBhkZWLiMhM4tEIl69roq0+wU+PniMZi2jXRYULRXBwzt000/1mFgPeALxwhm0c93+eMrOvAruAi4KDc+5O4E6Avr4+9Z2JiCwzM2Nda5rGdJxHnj7LwHCOtvqEBk5WqErZVXETcNA5d6zUnWZWb2YNU9eBm4H9K1ifiIjMojEV/+Wui+Fc0OXIAlVKcLiNabspzGyNmd3j3+wEfmBmjwI/Ab7pnPv2CtcoIiKziEcj/MraJrqaUpwZUXioRKHYVTEb59zbSyw7DtziXz8CvGCFyxIRkQWIRIwXrGvm+0/2M5IrUJ+siI8i8VVKj4OIiFSRVDzKzo2tjOQLjE/oaItKouAgIiKBaE4nuGp9C6dHdJ6HSqLgICIigVnXWkdPe4bTGu9QMRQcREQkMGbGjjWNNNclOD82HnQ5MgcKDiIiEqhYNMILL2lhYnKSsfxE0OXILBQcREQkcPXJGC/qbiU/OUH/cJaJSY15CCsFBxERCYX2hhQ3XtrJpasbOTOS49xYHqdBk6Gj4CAiIqERj0bY0tnAjds6ac8kOTmYZTRfCLosKaLgICIioVOfjLFzYyvXbekA4NTQGIVJne8hDBQcREQktNozSW7YuorL1jRxdnRcuy9CQMFBRERCLRoxNq1q4MZLV9GaTnByKEt2XEdfBEXBQUREKkJ9Msau7lau7m4jNzHBwLDOOBkEzSwiIiIVw8zoaq6jLZPk4HOD/PzUCO0NCWIRfQ9eKXqmRUSk4iRiES5f18yVG5o5PZwjV9Cui5Wi4CAiIhVrY3s91/S0MTg2rsM2V4iCg4iIVLTOpjqu39JBfmKSQc13sewUHEREpOI1pxNc39tBPGac0Uyby0rBQUREqkJ9MsaLN7XTnE5weljhYbkoOIiISNVIxaPs6m6lOZ1Qz8MyUXAQEZGqEo9G2NndQkMqztnRfNDlVB0FBxERqTrJmNfzkIpHOD+m8LCUFBxERKQqpeJRrulpJxY1HW2xhBQcRESkatUlvPBgBkNZhYeloOAgIiJVrT4Z45pNbUw4x3BOJ4laLAUHERGpeg2pOC/e1E6+MMGIwsOiKDiIiEhNaKqLs7u3g1xhQqenXgQFBxERqRlNdXF2b+4gm1d4WCgFBxERqSlN6TjX9rYzpvCwIAoOIiJSc5rTCa7d3M5ofoKxvKbkng8FBxERqUkt9Ql2b25nNF9gOKueh7kKTXAws181s8fNbNLM+qbd9z4zO2xmh8zsFWUe321mPzazJ83sLjNLrEzlIiJSqVrqE1y3xZtV89RQlolJF3RJoRea4ADsB94APFC80My2A7cBO4BXAv/HzKIlHv9B4GPOuV7gLPBby1uuiIhUg6a6ONf1drCtq5HTwzn1PswiNMHBOXfAOXeoxF23Al9wzuWcc08Bh4FdxSuYmQEvA77sL/oM8LrlrFdERKpHNGJs6Wzghq2r1Pswi9AEhxmsBY4W3T7mLyvWBpxzzhVmWEdERGRGTelf9j6cGclxeiRHYWIy6LJCJbaSv8zMvgOsLnHX+51zXy/3sBLLpsfAuawzVcPtwO0AGzZsKPMrRUSkVk31PnQ1pTh2doynBkbIFyZIJ2JkkjG8Tu7ataLBwTl30wIedgxYX3R7HXB82joDQLOZxfxeh1LrTNVwJ3AnQF9fn/qhRESkpIZUnG1dcXpXZTgzkufIwAgnB7NEzGhNJ4hEajNAVMKuiruB28wsaWbdQC/wk+IVnHMO+FfgTf6itwHlejBERETmLBaNsKoxxdU9bdy8fTWbOuo5NZSlMFmbuzBCExzM7PVmdgy4Bvimmd0L4Jx7HPgi8DPg28DvO+cm/MfcY2Zr/E38MfCHZnYYb8zD3690G0REpLrVJaJsX9PE5euaGBiuzfEP5n1Zr019fX1uz549QZchIiIV6OiZUR5+5gwt6SSJWGi+h89oJFfg5it7Dk3mRi5d6DYqo6UiIiIhs741zdU9bZwfy5Mdr53TVis4iIiILNDqpjpevLmdkVyhZibMUnAQERFZhPZMkt297WTHa2PCLAUHERGRRWpOJ7i6p42h3HjVD5hUcBAREVkCbZkkL1jXzMBwjmo+8EDBQUREZIlc0pampyPDwHAu6FKWjYKDiIjIEjEzdqxppCWd4PxYPuhyloWCg4iIyBKKRSP0bWzFQVUeaaHgICIissTqElFe1N3GcLZQdYMlFRxERESWQWt9gis2NDMwkmNisnoGS67o7JgiIiK1ZENrmnxhksePn6cxlaAuEQ26pEVTj4OIiMgyMTN6OxvY3dtBfmKCs6OVP2BSwUFERGSZtWeS3LB1Fa3pOCeHshW960LBQUREZAWk4lF2dbexo6uR/uFsxZ6eWmMcREREVkgk4u26aK1P8MgzZ+kfGicSMTLJGMlYZYx/UHAQERFZYW2ZJDdu62QwO86poRy/ODPC+aFxDKhPxkjFo0TMyj7eOcfY+ASjuQKTQGMqTiq+MsFDwUFERCQAkYjRnE7QnE7QuyrDcK7A6eE8x86OcmYkjzfdhSNiRioeJRY1RnIT/vgIR1smwaaOZmJRY//x8wzlxmlNJ4lGygeOpaDgICIiEjAzoyEVpyEVZ2N7PZOTjlG/R+H82Dinh/OMjk+wsS3NqsYUTXVxErFfDlPsbEzx1MAIB08MEotGaK6LYzP0WCyGgoOIiEjITI17yCRjrGpM0ds58/rxaIQtnQ2sba7j4HOD/OLMKJlknExy6T/mdVSFiIhIlahPxnjhJa1c39tBPGqcHMqSHV/aozcUHERERKpMWybJ9b0d7NrYwvjEJP1DWcaXaM4M7aoQERGpQpGIsaY5zaqGFEfPjvGz4+cZG198eFBwEBERqWKxaITu9nq6mlIc6R8GN7GofRfaVSEiIlIDUvEo29c04cZzY4vZjoKDiIiIzJmCg4iIiMyZgoOIiIjMmYKDiIiIzJmCg4iIiMyZgoOIiIjMWWiCg5n9qpk9bmaTZtZXtPzlZvawme3zf76szOPvMLNnzWyvf7ll5aoXERGpDWE6AdR+4A3A305bPgC8xjl33MwuA+4F1pbZxseccx9ZxhpFRERqWmiCg3PuAHDRNKDOuZ8W3XwcSJlZ0jmXW8HyREREhBDtqpijNwI/nSE0vNPMHjOzT5lZy0oWJiIiUgtWNDiY2XfMbH+Jy61zeOwO4IPAO8qs8jfAJuAK4ATw0TLbud3M9pjZnv7+/gW2REREpDat6K4K59xNC3mcma0Dvgr8hnPu52W2fbJo/U8C3yiz3p3AnQB9fX1uIfWIiIjUqtDvqjCzZuCbwPuccz+cYb2uopuvxxtsKSIiIkvInAvHl24zez3wcaADOAfsdc69wsz+BHgf8GTR6jc7506Z2d8Bn3DO7TGzz+LtpnDA08A7nHMnZvmdQ8ChpW/NimvHO/qk0lVDO6qhDVAd7aiGNoDaESbV0AaArc65hoU+ODTBIQhmtsc51zf7muGmdoRHNbQBqqMd1dAGUDvCpBraAItvR+h3VYiIiEh4KDiIiIjInNV6cLgz6AKWiNoRHtXQBqiOdlRDG0DtCJNqaAMssh01PcZBRERE5qfWexxERERkHmo2OJjZK83skJkdNrP3Bl3PXJjZejP7VzM74M8k+gf+8oqbGdTMnvZnPN1rZnv8Za1m9s9m9qT/M9SnDTezrUXP+V4zGzSzd4f99fBPyX7KzPYXLSv53Jvnf/nvk8fM7KrgKr9QmXZ82MwO+rV+1T8PDGa20czGil6TTwRX+YXKtKPs35CZvc9/PQ6Z2SuCqfpCZdpwV1H9T5vZXn95KF+LGf6/VtR7Y4Z2LN17wzlXcxcgCvwc6AESwKPA9qDrmkPdXcBV/vUG4AlgO3AH8F+Crm+ebXkaaJ+27EPAe/3r7wU+GHSd82hPFHgOuCTsrwdwPXAVsH+25x64BfgWYMDVwI+Drn+WdtwMxPzrHyxqx8bi9cJ0KdOOkn9D/vv9USAJdPv/x6JhbMO0+z8K/GmYX4sZ/r9W1HtjhnYs2XujVnscdgGHnXNHnHN54AvArPNlBM05d8I594h/fQg4QPkpxivRrcBn/OufAV4XYC3zdSPwc+fcM0EXMhvn3APAmWmLyz33twL/6DwPAs124VlaA1OqHc65+5xzBf/mg8C6FS9snsq8HuXcCnzBOZdzzj0FHMb7fxaomdpgZgb8GvD5FS1qnmb4/1pR741y7VjK90atBoe1wNGi28eosA9gM9sIXAn82F9UaTODOuA+M3vYzG73l3U6/2yf/s9VgVU3f7dx4T/GSns9yj33lfxe+U28b4RTus3sp2Z2v5ldF1RR81Dqb6gSX4/rgJPOueKz/4b6tZj2/7Vi3xslPiemLOq9UavBwUosq5jDS8wsA/wT8G7n3CBznBk0ZK51zl0FvAr4fTO7PuiCFsrMEsBrgS/5iyrx9SinIt8rZvZ+oAB8zl90AtjgnLsS+EPg/5pZY1D1zUG5v6FKfD3ewoWhOtSvRYn/r2VXLbEsNK9FuXYsxXujVoPDMWB90e11wPGAapkXM4vj/TF8zjn3FfBmBnXOTTjnJoFPEoKuy9k45477P0/hzXy6Czg51dXn/zwVXIXz8irgEefP0FqJrwfln/uKe6+Y2duAVwNvdf5OXL9r/7R//WG8sQFbgqtyZjP8DVXU62FmMeANwF1Ty8L8WpT6/0oFvjfKtGPJ3hu1GhweAnrNrNv/tngbcHfANc3K31f498AB59xfFC2vqJlBzazezBqmruMN2tmP9xq8zV/tbcDXg6lw3i74RlVpr4ev3HN/N/Ab/gjyq4HzbpbJ44JkZq8E/hh4rXNutGh5h5lF/es9QC9wJJgqZzfD39DdwG1mljSzbrx2/GSl65uHm4CDzrljUwvC+lqU+/9Khb03ZvicWLr3RtAjQIO64I2IfQIvXb0/6HrmWPNuvK6wx4C9/uUW4LPAPn/53UBX0LXO0o4evJHhjwKPTz3/QBvwXbyZUL8LtAZd6xzakgZOA01Fy0L9euCFnBPAON63pt8q99zjdcf+tf8+2Qf0BV3/LO04jLffeer98Ql/3Tf6f2uPAo8Arwm6/lnaUfZvCHi//3ocAl4VdP3l2uAv/wfgd6atG8rXYob/rxX13pihHUv23tCZI0VERGTOanVXhYiIiCyAgoOIiIjMmYKDiIiIzJmCg4iIiMyZgoOIiIjMmYKDSADMzJnZZ4tux8ys38y+scDtNZvZ7xXdvmGh2yqz/TVm9uWl2t5K8Gf9+/eLePzbzWzNUtYkUg0UHESCMQJcZmZ1/u2XA88uYnvNwO/NutYCOeeOO+fetFzbXyYbgQUHB+DtgIKDyDQKDiLB+Rbw7/zr088+2WpmX/MnOXrQzC73l9/hT3r0PTM7Ymb/2X/IB4BNZrbXzD7sL8uY2ZfN7KCZfc4/oxxm9gEz+5m/7Y9ML8rMXuJvZ68/8U2D/+19v3//283sK2b2bTN70sw+VPTYV5rZI2b2qJl9119W79f8kL+9i2ai9XtI7jezL5rZE36NbzWzn5jZPjPb5K/3GjP7sb+d75hZZ7ma/efkOn/Ze8wsamYf9ut4zMzeUfT7/8j/PY/6v/tNQB/wOf/xdWZ2o7/tfX57kv5jnzazPzezH5nZHjO7yszuNbOfm9nv+Ot8trjd/uvx2rn+oYiEStBnudJFl1q8AMPA5cCXgRTemdxuAL7h3/9x4L/7118G7PWv3wH8G5AE2vHOWhnH+3a9v2j7NwDn8c6fHwF+hHdGuVa8Mw5OnfytuURt/w9vEjKADBAr3j7eN/EjQJNf+zN45+zvwDszXbe/3tQZ9v4c+A9Tvw/vjK31037nDcA5oMtv27PAn/n3/QHwl/71lqLa/xPw0Rlqfv759JffDvyJfz0J7AG68eYa+TcgPa3u7+GfDdBv51Fgi3/7H/EmDwJ4Gvhd//rH8M7Y1+A/H6f85S8BvuZfbwKeAmJB/x3qostCLupxEAmIc+4xvA/ktwD3TLt7N95ph3HO/QvQZmZN/n3fdN7ENAN4E+50lvkVP3HOHXPeREl7/d81CGSBvzOzNwCjJR73Q+Av/N6MZudcocQ633XOnXfOZYGfAZcAVwMPOOee8us+4697M/BeM9uL92GcAjaU2OZDzrkTzrkc3ml87/OX7/NrBy8I3Wtm+4D/CuyYR803480tsBdvmuE2vPPy3wR82vnn7y+qu9hW4Cnn3BP+7c8AxTO6Ts11sw/4sXNuyDnXD2TNrNk5dz+w2cxW4b3e/1SmRpHQU3AQCdbdwEe4cNphmHnK3lzRsgm8b9elXLSe/2G1C2/mvNcB377olzj3Abxv83XAg2Z26Vy27ddc6hz2BrzROXeFf9ngnDswyzYni25P8ss2fhz43865XwHegRdC5lqzAe8qqqPbOXffDHVPf+xMimud3o6p2j8LvBX4j8CnZ9meSGgpOIgE61PA/3DO7Zu2/AG8DxnM7AZgwDk3OMN2hvC6x2dkZhm8CbnuAd4NXFFinU3OuX3OuQ/ideeX+hAu5UfAS8ybtREza/WX3wu8q2iMxZVz3F4pTfxyEOnUjIXlap7+nNwL/K55Uw5jZlvMm531PuA3zSw9re7ixx8ENprZZv/2rwP3z7P2f8B7znHOPT7Px4qERrlvKiKyApw33fBflbjrDuDTZvYY3u6Et5VYp3g7p83sh/4Axm8B3yyzagPwdTNL4X2Lfk+Jdd5tZi/F60n4mb+9baS9PgAAANNJREFUrhLrTa+h38xuB75iZhG83SgvB/4n8JfAY354eBp49WzbK+MO4Etm9izwIN4YhXI1TwIFM3sU70P7r/B2eTzi19EPvM45920zuwLYY2Z5vN1G/81/zCfMbAy4Bq+n4EtmFgMeAj4xn8KdcyfN7ADwtYU1XSQcNDumiMgK8Hs09gFXOefOB12PyEJpV4WIyDIzs5vwdnd8XKFBKp16HERERGTO1OMgIiIic6bgICIiInOm4CAiIiJzpuAgIiIic6bgICIiInOm4CAiIiJz9v8BLiq9Tsvhb8oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "beta_hpd = np.percentile(time_varying_trace['beta'], [2.5, 97.5], axis=0)\n",
    "beta_low = beta_hpd[0]\n",
    "beta_high = beta_hpd[1]\n",
    "ax.fill_between(interval_bounds[:-1], beta_low, beta_high,\n",
    "                color=blue, alpha=0.25);\n",
    "beta_hat = time_varying_trace['beta'].mean(axis=0)\n",
    "ax.step(interval_bounds[:-1], beta_hat, color=blue);\n",
    "ax.scatter(interval_bounds[last_period[(df.event.values == 1) & (df.metastized == 1)]],\n",
    "           beta_hat[last_period[(df.event.values == 1) & (df.metastized == 1)]],\n",
    "           c=red, zorder=10, label='Died, cancer metastized');\n",
    "ax.scatter(interval_bounds[last_period[(df.event.values == 0) & (df.metastized == 1)]],\n",
    "           beta_hat[last_period[(df.event.values == 0) & (df.metastized == 1)]],\n",
    "           c=blue, zorder=10, label='Censored, cancer metastized');\n",
    "\n",
    "ax.set_xlim(0, df.time.max());\n",
    "ax.set_xlabel('Months since mastectomy');\n",
    "\n",
    "ax.set_ylabel(r'$\\beta_j$');\n",
    "\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coefficients $\\beta_j$ begin declining rapidly around one hundred months post-mastectomy, which seems reasonable, given that only three of twelve subjects whose cancer had metastized lived past this point died during the study.\n",
    "\n",
    "The change in our estimate of the cumulative hazard and survival functions due to time-varying effects is also quite apparent in the following plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "tv_base_hazard = time_varying_trace['lambda0']\n",
    "tv_met_hazard = time_varying_trace['lambda0'] * np.exp(np.atleast_2d(time_varying_trace['beta']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.step(interval_bounds[:-1], cum_hazard(base_hazard.mean(axis=0)),\n",
    "        color=blue, label='Had not metastized');\n",
    "ax.step(interval_bounds[:-1], cum_hazard(met_hazard.mean(axis=0)),\n",
    "        color=red, label='Metastized');\n",
    "\n",
    "ax.step(interval_bounds[:-1], cum_hazard(tv_base_hazard.mean(axis=0)),\n",
    "        color=blue, linestyle='--', label='Had not metastized (time varying effect)');\n",
    "ax.step(interval_bounds[:-1], cum_hazard(tv_met_hazard.mean(axis=0)),\n",
    "        color=red, linestyle='--', label='Metastized (time varying effect)');\n",
    "\n",
    "ax.set_xlim(0, df.time.max() - 4);\n",
    "ax.set_xlabel('Months since mastectomy');\n",
    "\n",
    "ax.set_ylim(0, 2);\n",
    "ax.set_ylabel(r'Cumulative hazard $\\Lambda(t)$');\n",
    "\n",
    "ax.legend(loc=2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RERERmZLGpWXYObfFOfdU9LgNeB6Y32ezdwK3udCfgbooiD4d+K1zblcUAP8WePt41FtERERERESmpnEfM2xmS4Cjgcf7rJoPvNbjeUO0bKDlIiIiIiIiIsMSG8+DmVkVcDfwGedca9/V/ezi9rK8v/IvBi4GqKysPPbQQw8dQW1FRGQ6as0WMCBX6sThMDw2vvxyW1AIaspdt8lu1qxZbsmSJeWuhoiITAF//etfdzrnZo+kjHELhs0sThgI3+6c+49+NmkAFvZ4vgDYHC1f1Wf5Q/0dwzl3E3ATwIoVK9yTTz454nqLiMj08pvnNrM19yJthUZq4nUUA8clp5yxo9z1mgqWLFmC/jaLiMhoMLMNIy1jvLJJG/DvwPPOuW8PsNl9wIeirNLHAy3OuS3AfwJvM7N6M6sH3hYtExERGVXFoMjWzHp25bZRHastd3VERERkDI1Xy/CJwAeBZ81sdbTsy8AiAOfcjcCvCTNJvwx0Ah+O1u0ys/8P+Eu039XOuV3jVG8REZnCnHN0FjtpzjazpWMLOzI72NTRyH6Vcwjv44qIiMhUNS7BsHPuj/Q/9rfnNg74xADrbgFuGYOqiYjIJFIKSmRLWToLnbTn28kFOUquRBAElIISJUoELgDCQHdf2gvtZItZzIx0LM2M1AyqYw7PG/f8kiIiIjLOxjWBVrkVCgUaGhrIZrPlropMAKlUigULFhCPx8tdFZFpzTlHtpQlU8yQKWTIlrI45whcgCP8txgUac41015ox0U5FD08Yl4MwzCzXv/2tLcW3lQsRXWiund9KMNUCyIiIjLuplUw3NDQQHV1NUuWLFH3t2nOOUdjYyMNDQ0ccMAB5a6OyJjqLHSSKWaGvb/D4Zyj5EqUXIl8MU8hKFBwhRHVywWOtkIbrbnW3a25OHzP3yOwNTOSXpKZqZlj+vt7MK3JIiIiMjVMq2A4m80qEBYgvLCeOXMmO3YoQaxMbYELeHzr42QLI+wRY4CLglXz8TwPbxTaT+N+nLpUHZ5NjLbYMBbW3wgREZHpYFoFw7D37nIyveizINPBruwuMoUMsytGNA3ftBG2DKt1WEREZDqYGLfip5Gqqqpez2+99VYuu+yyIZWxZMkSdu7cOeK63Hvvvaxdu3bE5fTnO9/5Dp2dncPat2+9rrjiCn73u9+NuE59X3uR6WBDywZSsVS5qzFpKAwWERGZPhQMT2OTJRi++uqrOe2000araiLTRmehk22ZbVTFdSNosBQMi4iITB8KhieQX/7yl6xcuZKjjz6a0047jW3btgHQ2NjI2972No4++mg+9rGPDZjgpaqqin/+53/mqKOO4vjjj+/ef8OGDZx66qkceeSRnHrqqWzcuJE//elP3HfffXzuc59j+fLlvPLKK73KuvDCC7n00ks5+eSTWbp0KQ8//DAXXXQRy5Yt48ILL+ze7oEHHuCEE07gmGOO4dxzz6W9vZ3rr7+ezZs3c/LJJ3PyyScDcOmll7JixQoOP/xwrrzyyu79v/jFL3LYYYdx5JFH8tnPfrbfel144YX84he/4Mknn2T58uUsX76cI444orub8yuvvMLb3/52jj32WN70pjfxwgsvALBu3TpOOOEE3vCGN3D55ZePzpskMols6diCh6chAUPgFA4DYGa3mNl2M3tugPVmZteb2ctm9oyZHTPedRQRERmpaTdmuMtXf7mGtZtbR7XMw/av4cqzD9/rNplMhuXLl3c/37VrF+eccw4AJ510En/+858xM26++Wa+8Y1v8K//+q989atf5aSTTuKKK67gV7/6FTfddFO/ZXd0dHD88cdzzTXX8PnPf54f/OAHfOUrX+Gyyy7jQx/6EBdccAG33HILn/rUp7j33ns555xzOOuss3jPe97Tb3lNTU38/ve/57777uPss8/m0Ucf5eabb+YNb3gDq1evZsGCBXzta1/jd7/7HZWVlVx77bV8+9vf5oorruDb3/42Dz74ILNmzQLgmmuuYcaMGZRKJU499VSeeeYZFixYwD333MMLL7yAmdHc3ExdXd2A9VqxYgWrV68G4HOf+xxvf/vbAbj44ou58cYbOfjgg3n88cf5+Mc/zu9//3s+/elPc+mll/KhD32I733ve4N4B0WmjlJQYl3LOmqSNeWuyuSiBFpdbgVuAG4bYP0ZwMHRz0rg/0T/ioiITBrTNhgul3Q63R3QQThm+MknnwTCqZ/e+973smXLFvL5fPeUP4888gj/8R//AcA73vEO6uvr+y07kUhw1llnAXDsscfy29/+FoDHHnuse/8PfvCDfP7znx9UXc8++2zMjCOOOIK5c+dyxBFHAHD44Yezfv16GhoaWLt2LSeeeCIA+XyeE044od+y7rrrLm666SaKxSJbtmxh7dq1HHbYYaRSKT7ykY/wjne8o7vu+3LXXXfx1FNP8cADD9De3s6f/vQnzj333O71uVwOgEcffZS77767+7y/8IUvDKp8kalgV3YX+VKe2mRtuasyqYQdb9Q67Jx7xMyW7GWTdwK3ubCr0p/NrM7M5jnntuyt3M0tw5/iS0REZLRN22B4Xy245fDJT36Sf/zHf+Scc87hoYce4qqrrupeN5hujvF4vHs73/cpFov9bjfYLpPJZBIAz/O6H3c9LxaL+L7PW9/6Vu644469lrNu3Tq+9a1v8Ze//IX6+nouvPBCstkssViMJ554gv/6r//izjvv5IYbbuD3v//9Xstas2YNV155JY888gi+7xMEAXV1db1uMAznXEWmmnWt60jH0uWuxqTjoHtuY9mr+cBrPZ43RMv2CIbN7GLgYoD0gpk8sfFlzDw8MwwP33yq4tX4XqzPfrvb6Hv+Lu/5a71ruUFYXtc+1v/7aAZxzyMRC398T++1iMh0Nm2D4YmopaWF+fPnA/CjH/2oe/mb3/xmbr/9dr7yla/wm9/8hqampiGV+8Y3vpE777yTD37wg9x+++2cdNJJAFRXV9PW1jbs+h5//PF84hOf4OWXX+aggw6is7OThoYGXve613WXPWvWLFpbW6msrKS2tpZt27bxm9/8hlWrVtHe3k5nZydnnnkmxx9/PAcddNBe69XS0sJ5553HbbfdxuzZ4TQxNTU1HHDAAfz85z/n3HPPxTnHM888w1FHHcWJJ57InXfeyQc+8AFuv/32YZ+nyGTTUehgZ+dOZqVnlbsqk84AKRlkT/1Fkf2+es65m4CbACoW17kHXn0CcJgznIW3HzzzmJGYR11iDmm/GtsjpYmLyuodDHdXxRxRUQRubx3dw227ahqPeVTEfSqTMaqSMapSMZIxn2TcI+H3n1Yl5hmxAdaJiMjkomB4Arnqqqs499xzmT9/Pscffzzr1q0D4Morr+T888/nmGOO4S1veQuLFi0aUrnXX389F110Ed/85jeZPXs2P/zhDwE477zz+OhHP8r111/PL37xCw488MAhlTt79mxuvfVWzj///O6uyV/72td43etex8UXX8wZZ5zBvHnzePDBBzn66KM5/PDDWbp0aXe36ra2Nt75zneSzWZxzvG///f/7rdeXe699142bNjARz/60e5lq1ev5vbbb+fSSy/la1/7GoVCgfPOO4+jjjqK6667jve9731cd911/P3f//2Qzk1kMtvcthnPlDhr+BQRD0IDsLDH8wXA5n3t5IAHnqzrFdAescjn6AMgU9zJ1vw2El6cOekFzErtT9If22nBSoGjUApo6iiwrTVHKQiAsFXZRf0E+jsLM0jHY6TiHqm4T0XSpzoZIxn3ScV9krEwmNZ3UERkYrOBMhNPditWrHBdY3G7PP/88yxbtqxMNZKJSJ8JmWqKQZEHNz5IVaKKmKf7nUPVkS/yt43N1Kbj3cuKgeOSU854tdhWHNodw0kuGjN8v3Pu9f2sewdwGXAmYeKs651zx+2rzIolde6Yj9+O74dB4oYd4TXI4tm7g0bnHK9bkGP5EsfS6sOpT80e+cmMssA5SoGjWAr/LQQBxVLvQNqsq+u24VnYpduA2oo4i2dUMqMyQSKmFmYRkeEys78651aMpAxdKYmITCGNmUbyQV6B8DA5p+mVAMzsDmAVMMvMGoArgTiAc+5G4NeEgfDLQCfw4cGUm4jB3x1fYlZlBQBPvlri2Y2lXttsawGzFCsPhBdbVzOvsIj5lQdOqM+0Z4bnG3F/4G2cc9HnKXpO+KSls8DjLY14BvPq0iyqr6CuIkHf4ctmpjHNIiJjbOL8ZRERkX4NpQfPupZ1VMYrx7A2U5ziYACcc+fvY70DPjHUcg0jGQ/IFkukYj4rloY/Pf3woTxbmx0/ecTA1VByO/FsF6lYJW8+aC6nLps71MOWhUUJvXosAaDa96hOxQmco7Etz6amzIBjnBfPrOTQedUkY3uJukVEZNgUDIuITECZYobmbDNbOrawo3MHJVfa905AyZXYr3K/Ma7dVOaUTXoMmRkzKo0drWEw3J8jFvlA9Hk38C1G4AI27OzgwWATpxw6Z0qMxfXMqEnHqSHe7/rAOTbu6mBLS4blC+uYW5OaEuctIjKRKBgWERlHpaBEtpQlU8wQuGCP9R35DjZ1bKI13wpA2k9Tl6rDM40tHA9TNI3GhGEYVWmfHa0MmJ6qv9ZigB8+mOO1XTm+/H+fJOWnuwPDEw+cNWlai4fCM2NWVYpsocRjr+xi0cw0h+9fS2pvfbNFRGRIFAyLiIyhbDFLY6aRplwTzdlm2gptYXKdvbQ+VsYrmZ2eeEmDpoMApzHDYyhXynHLmh+QLxpB4PDMWFZ3DEfOeOM+9z1icQwoUQzydLoS6Vglr+3KAjunZDDcJRX3mVvjsbUly9aWLIfvX0ttOk5F0lf3aRGREVIwLCIyBrLFLBtbN/Jqy6sELiDhJ0j5KWamZqqr4wSnbtJjJxULp0pK+B6dpRKNuU3QzKCC4d0txgk6im04l+O+x+rGuMYTQ9i9PEm+GPBMQzNmhnOOioTPzKokMysT+IOc+9gzqEsnSCcUSIuIKBgeZ2bGBz7wAX784x8DUCwWmTdvHitXruT+++8fcL/Vq1ezefNmzjzzzCEfs7m5mZ/+9Kd8/OMfB2Dz5s186lOf6jWH73BcddVVVFVV8dnPfnZE5YhMJT2DYIC6ZB2+p4vOyULZpMfWkpolfOaYz+BbnNUb2/jN5n8bVjmVsWpypSwdxXZ2tca4+v41g9pvsnepTsQ8Zlfvnns5XwzY3pbjtabOISV/c8CsqgSLZlQyqyqpwFhEpi0Fw+OssrKS5557jkwmQzqd5re//S3z58/f536rV6/mySefHHYw/P3vf787GN5///1HHAiLTGb5Up4NLRsouiKloESJEi5w4b8jCYQc7MzsBBQET1YKg8debbKWllwLs6tTlJzDH2ZPiaSfYvmiPKs3FsiXsiT81F6339DYyVTrUp2IedFcxf0n4RqIc47OfImnNzZ1B8bz6yqoTcepSsWID7KVWURkslMwXAZnnHEGv/rVr3jPe97DHXfcwfnnn88f/vAHADo6OvjkJz/Js88+S7FY5KqrruKMM87giiuuIJPJ8Mc//pEvfelLHHDAAXzmM5/pDqp/+MMfcsghh7BmzRo+/OEPk8/nCYKAu+++m8svv5xXXnmF5cuX89a3vpVPfOITnHXWWTz33HN85CMf4cknnwRg06ZNXHbZZVx55ZV885vf5K677iKXy/Gud72Lr371qwBcc8013HbbbSxcuJDZs2dz7LHHlu11FBmuHZ07WLtrLZXxynD6k67/RY9HQkHw5BYm0FI36bFUm6xlR+cOZldXha/3CF7uNxyU4NgDfVoKuzig+lDmphcOuO1gW4+nAzOjMhmjMhnDOUemUOKZTc3dWc3q0gnmVCd7z39s4RACz6C+IoGnOZBFZAqYtsHwtU9cywu7XhjVMg+dcShfOO4L+9zuvPPO4+qrr+ass87imWee4aKLLuoOhq+55hpOOeUUbrnlFpqbmznuuOM47bTTuPrqq3nyySe54YYbAGhtbeWRRx4hFovxu9/9ji9/+cvcfffd3HjjjXz605/m/e9/P/l8nlKpxNe//nWee+45Vq9eDcD69eu763LzzTcDsGHDBk4//XQuvPBCHnjgAV566SWeeOIJnHOcc845PPLII1Rc/XYeAAAgAElEQVRWVnLnnXfy9NNPUywWOeaYYxQMy6S0pWMLNYkaqhJV5a6KTDSu+z8yRqoT1ZRcibpUHLORv9qe+dTE61nf9jyGx5z0vntbyW5mRkUiRkUivCR0zpErBryyo4PAteGcgbnuN6oUwIFzKjlifq3yH4jIpDdtg+FyOvLII1m/fj133HHHHt2eH3jgAe677z6+9a1vAZDNZtm4ceMeZbS0tHDBBRfw0ksvYWYUCgUATjjhBK655hoaGhp497vfzcEHH7zP+mSzWc4991xuuOEGFi9ezHe/+10eeOABjj76aADa29t56aWXaGtr413vehcVFRUAnHPOOSN6HUTKoRgU2ZnZSX2qvtxVkQlI44XHXjqWDlsYPSPhe+SLe04xNlS++VTH6nm1dQ2e+cxKaa7t4TIzUnF/wCmcAud4ZXs7Mc9j2bxqBcQiMqlN22B4MC24Y+mcc87hs5/9LA899BCNjY3dy51z3H333RxyyCG9tn/88cd7Pb/88ss5+eSTueeee1i/fj2rVq0C4H3vex8rV67kV7/6Faeffjo333wzS5cu3WtdLrnkEt797ndz2mmnddfhS1/6Eh/72Md6bfed73xHf/Rk0mvLtxEQaN5e6VcYCuv33FhKx9LdNx3ivkduFIJhAN+LUR2v5+XWZ/HwmJGaMyrlSm+eGXOqU7y4tZWYb7xubnW5qyQiMmy6GiyTiy66iCuuuIIjjjii1/LTTz+d7373u7hw4BpPP/00ANXV1bS1tXVv19LS0p1469Zbb+1e/uqrr7J06VI+9alPcc455/DMM8/ssW9P3/ve92hra+OLX/xirzrccssttLe3A+FY4u3bt/PmN7+Ze+65h0wmQ1tbG7/85S9H/kKIjLPGbCM+GtMr/XM9/itjI+bFSMfSFEoFfM+IeUZHvjRqZVfHanmp9W9s6niVLZ0bun/ypRyFUr7776sMn+cZs6tTrNnUyqs72stdHRGRYZu2LcPltmDBAj796U/vsfzyyy/nM5/5DEceeSTOOZYsWcL999/PySefzNe//nWWL1/Ol770JT7/+c9zwQUX8O1vf5tTTjmle/+f/exn/OQnPyEej7PffvtxxRVXMGPGDE488URe//rXc8YZZ/CJT3yie/tvfetbxONxli9fDoStxJdccgnPP/88J5xwAgBVVVX85Cc/4ZhjjuG9730vy5cvZ/HixbzpTW8a41dJZPRtbt9MZbyy3NWQCcoFDsVKY68uWUdzrhmAxtxm7t34fWI9EjItqztmUHMP9yfmxamK1bKlc0Ov5blSAoejpbCLusTM4VdeAPA9Y1Z1gr81NBP3PBbOrCh3lUREhsym6h3SFStWuK4syV2ef/55li1bVqYayUSkz8T0kilmePC1B5mdnl3uqsgEta0lw8s72qlLJ7qXFQPHJaec8WqxrXhgGas2JXT9bX61+VVeanqJZ3Y+w+NbHqczX6QYhNMs7chuYnZqPu9detmoHvuHD+XZ2hwwtxYqYzXdveEn+9zD5VYsBezsyHHMwnoWzqhQlmkRGTdm9lfn3IqRlKGWYRGZNlpyLZjThZoMrDlTIO6rG/1Y68oovWrhKlYtXEUmX+KpjbuoSSX4+bobxuSYRywK39diUKTgCsQtPiXnHh5vMd9jZmWSp19rYv2uTo6YX8uMysS+dxQRmQAUDIvItLGtYxuJmC7SpH/5Yomd7Xlq0vFyV2XKS8VSvZ6nEz4L6ytoaMqM2TFXLPVZsdSnEEAhaOPImSdwza9eHLPjTSdx32NuTZr2bJGHX9zB4llpDt2vpnu6JhGRiUq/pURkWghcwLbObdQkaspdFZmgmjrygFNmyXHQNb2Sc657loL96lJsbsngGNt83nEvQWexnZ3ZLWN4lOmpKhWjMumzpTnLpqYsh8ytoiI5fpeanhm+Z5iBb4YX/fTLwCz8rJkZY92726JPdVd1kjFPM3SITADTLhju+YdXprepOl5e+teWb6MYFPE9dYGVPTnn2NySJR2fdn8WyyLmxaiIV1AMisT9sCU+4fscMLOS0muuVzKtsVAZq6Gh/RWcm6VrglFmZsyoTFIMAl7c1r7H39qx+str0X8McC4KPm0vf+sNzBmOsb8udLjd9bLw3zk1KY5cUKvWc5EyG5dvoJndApwFbHfOvb6f9Z8D3t+jTsuA2c65XWa2HmgDSkBxJIOkU6kUjY2NzJw5U3/8pjnnHI2NjaRSqX1vLFNCU7ZJcwvLgDryJTpyReor1I1+vNQmamnKNXUHwwCzqlN4BsEY36yMeTFKxRL5IEfS19+BsRDzPGZVJctdjQmrqTPPfz2/nSMX1LKwXonHRMplvG5H3QrcANzW30rn3DeBbwKY2dnA/3TO7eqxycnOuZ0jrcSCBQtoaGhgx44dIy1KpoBUKsWCBQvKXQ0ZJ1vat1AR19Qf0r+d7Vl8XYyOq9pkLVs7t1JFVfcy3zPScX/U5h3em6p4LflSli3NJa6+f82g9lHmaRktdekEhVLA0xubaGjKcOSCWqpTylcgMt7GJRh2zj1iZksGufn5wB1jUY94PM4BBxwwFkWLyASWL+VpzjczM6W5RWVPpcCxtSVHpborjquqRBWun06zMd8j5gW054pUjeF4U998li0s8fLmwbVeKvO0jLauxGMtmQIPvrCdA+dUkY77JGIevheOf455HnXpuFqORcbIhPrLb2YVwNuBnpMLOuABM3PAvznnbtrL/hcDFwMsWrRoLKsqIpNIa75V+QJkQK2ZAsUgwPcm1J/EKS8dSw+4rjG/mfsa/g8GvRIgLas7hiNnvHHU6nDCQZW8fnEzR844jFRs7z1HBtt6LDJUtek4xcBn/c5OnHO7hwkYBAEsnlnBEfNrifka6iMy2ibaX/6zgUf7dJE+0Tm32czmAL81sxecc4/0t3MUKN8EsGLFCmVHEhEAtndu7zUuUaSnLa0ZEppbeNylYilweya2XDlvJRC22Lfnit0Zf3dkN0EzoxoMe+bheT5bM6+xpPqQfW6/obGz36BY3adlpGKe1+/8zM45XtvVSWe+xLGL60nF9btKZDRNtGD4PPp0kXbObY7+3W5m9wDHAf0GwyIifTnn2NK+hcp4ZbmrIhNQvliiqSNPbVqJs8ZbV0bpQlAg4e9+/VctXMWqhasA2NGW5YWtbdSlE/x83Q1jUo9Kv5rtmQbmVSwi6Q/cWn3igbOAPdOXqPu0jCUzY3Z1iqaOHI++vJOVS2eO6fABkelmwnybzKwWeAvwgR7LKgHPOdcWPX4bcHWZqigik1BHoYNcKUdNUvMLy552deTZPQOojLfaZC1N2aZewXBPs6tT5AoB63Z2jFkdPPMw89ie2cTCqoMG3O7UZXP7DXjVfVrGQ31lktZsgYdf3M4JB87qtxVZRIZuvKZWugNYBcwyswbgSiAO4Jy7MdrsXcADzrmef/HmAvdE3adiwE+dc/9vPOosIpNPtpglcEGvZY2ZRo0Vln4559jUnKEioW6H5VKXrGNrR++M0n3Nr0+TLQYUt4zd/MNVsWq2ZDayX8VC4t7QpwMaqPt0X+pOLSNRk4qTyZf440s7OGBWZa/x9GPJPEj4HgnfixLcGZ4X3kQ0MzzbPa9zVTKmzPwyqYxXNunzB7HNrYRTMPVc9ipw1NjUSkSmks5CJ3/c9EdKQe8pWQICqhPVZaqVTGQduSKZQol6dZEum6pEFQHBXrcxMw6YWUHMM0rB2KQD8cwH59iZ3cq8isVD2neg7tN9qTu1jIZ0wifmGw1NmXE7pgOCoCuxlwHhOH8XJfrqehw4x9LZVRy5oG7c6iYyUhOmm7SIyEg0Z5spuiKzK2aXuyoyCTjn2N6WwzdlZy2nlJ8a1Ha+75FO+HTmS7Rk8lSnE4z2O1cZq2Fzxzpmp+YTG0Jm8YG6T/el7tQyWuK+R13FxLuJFzjHqzvaWVhfQb26ccskoasAEZkStnVuG/SFtUxP+VKJps4863a089SGJjY1Z6hMqot0OaVjaTy8PYY39MczozLhM6cmTXNnnuIotxLHvBglV2JXbvuolisyXYTf0Th/a2gmGKNeHCKjTS3DIjLplYIS2zPbqUuqa5bsqakjz2tNnbRlCzjCKUxSMZ8ZFQqEy833fPar3I/GbCM1iX0nuTMzDpxdSU0yxks72kjFfVKx0XsfK2JVbOp4hVmpuWHXaREZkqpUjG1tWTbu6mTJLM3iIBOfgmERmfTa8m2UghKeurxKD6XA0dDUycbGTioSPrXphLJGT0D7V+3P5vbNMIhelRvbNvKNv3wDCN/fjnyRg6qP5rg5J41KXeJego5iK825Rmak5oxKmSLTzYyKBGs2tbBfbUrzIsuEp2BYRCa9xmyjAmHpJZMv8dL2NlqzBeoqEii56cRVn6rHs7Cr9N6+xyvnrez13PeM5sIWXm03Dqs9ftTmXq3wq2joeIW65KxR/70y2KzToMzTMnnFfQ9n8MKWNpYvUo8tmdgUDIvIpLelYwuVcXXHklBje47/3tqG55kyRU8CcS8+qK7SqxauYtXCVb2WXfvEtQTOUQwCSs7hj8JUMwk/RXO+kbZCE7WJmSMur8tgs06DMk/L5DejIsH6xg4Wzkgzs2ro05WJjBcFwyIyqeVKOVpzrcxKzyp3VaTMgsCxvrGDzc0ZqpJx4r6agyeLoXSV7sszY8nMStY1dozazY+UX8F/tzxDos+cw54Zi6sOpSZRP+QyB5t1GpR5WiY/M6MqGeNvDc285XVzNPewTFjqVygik1pLrgUXzXko01epFPDS9jY2N2eorUgoEJ5kenaVHo79atNUJHyyhdK+Nx6ElJ+m0q8iZvFeP845Xmx5mvZCy6gcR2Qqq0zGaMsWeHl7G00deZo787R0FmjNFmjPFctdPRFALcMiMslt69hG0lcXrOmsUAp4aWsbTZk8dRVKkjUZDbar9EB8zzhodjXPNDSTiPujcqff72eu4RgxwHix+WmW1a+gIlY1CkcSmbpmVCR5YWsb/721HYcDA3NG4BzHHTCDeXXpcldRpjm1DIvIpOWcY1vnNo0XnsbyxRLPb26lJVugTtmiJ7X5VfPJFXPD3r8mHWdeXZq2TH4Ua7WnpJ8i5sV5sfkpsqXOMT2WyGQX8z3mVKeYVZ1kdnWK2VXh46pUjBe3tuGc5iOW8lIwLCKTVluhjXwpT6yfFhyZ+rKFEs9tbqGzUKImFS93dWSE6lJ1I+oqDbBwRhrf9yiUhl/GYKT8CrpaiHOl7JgeS2QqqkjEaMkWaOwY25tXIvuiYFhEJq3mbHO5qyBl0p4t8mxDC8USVI/SlDpSXl1dpdsL7cMuI+H7HDi7krbs2I9HrIhVUXRFXmr5G4VAF/QiQ5WK+7y0bfjfd5HRoCsIEZm0NKXS9NTYnuOFra0kYz4Vcb/c1ZFRNL9q/pCzSm9s28i1T1zba1lHvkih6OibV++g6qNZOfekUahpqCpWQ1uhhVdan+N1tUfhmT6PIoNVnYyxvS1LS6ZAbVq9e6Q81DIsIpNSISiwK7OLdEzJN6aLIHBs3NXB2i2tVCbipBUITzlD7Sq9ct5KFlUv2mN5Ou5TkfBJx3f/NBe28Gr70xRKoztGsTpeS0t+F5s61o1quSJTnZkR9z3W7+wod1VkGlPLsIhMSi25ljArpaZUmhYKpYBXd7SzvS1HXTqBpqycmuJenHmV89iZ3TmorNKrFq5i1cJVgyr72ieuJVsokSuWiPuje/lTE69nU+c6KmM1zEjNGdWyRaay2nScDY0dHDy3ioqEwhIZf/rUicik1JhpxFeXxCmvFDg6ckVe3tFGrhBQr6mTprz9q/ZnU/umIXWVHizfM4rB6CfX8syjKlbDK23PkY6tJB0b+fCNDY2dXH3/mj2Wn3jgLE5dNnfE5YtMBJ4ZnhkbGjtZNm/o06qJjJSCYRGZdJxzbG7fTFVcc3xONaVSQGe+RFuuSFNHntZMgQBH3PeVMXqa6NlV2rPRHc3lecZYTeQS9xIUgwIvtTzDYfUriHnD/7yeeOAsYOceyzc0dgI7FQzLlFJbEeeV7e0snV1JMqab3DK+FAyLyKSTKWbIFDNUJRQMl0uuUKJQCggcOFz4r4PAOZxzBIGj6MKW3WCAlriSC7s/F4oB+WJAvhQQ9JhzMhXzqUrHldximunuKp3ZSU1ydFuKPDN8zyNwjElX+3SsktZCMxvaX2Rp9eHDHsZx6rK5/Qa8/bUUi0x2Mc8jcI7NzVkOmKWkmDK+FAyLyIQTuICOQgdtuTYas42UglKv9XlNY1IWhVJASybPtpYcTZk8HgY4wHC47mfhEguDWDPM6Ldrs5nhWdh11fc8qmK+xgILAAuqF7CpY9Ool2tAbSpGZ740ZgnYqmO17MhuoSpWS31yz/HDcS+hXAcifdSmE7y4rZVFMyrw9YdAxpGCYREpu3wpT2ehk7ZCG9s7t9OYaaQYFDGMRCyB10/bYH2qvgw1nX7yxRId+RI7WnPsbM8SELbY1qU1dlfGTn2qnrSfJlfKkfSTo1r2jMoETZ3tYxYMmxk18XrWtb/Aho7/7rXOOcfCyoPYv3LJsMsfaCxxfzS+WCaLRMyjOROwfmc7tRVjkDBgCDwzfDPMAz8a0+z1eqy/flOJgmERGRWloEQhKBC4gKIrUgpKlFyp3ylSnHN0FjppyjXRlG0iX8rjzIGDdCxNTaIG39O4odEQBI7OQonBDpQsBgEd+RKtmTxt2SKFUoADEr5PdUpZnGV8eOaxtHYpa3etJZke3WA4zFg7th9k33zqE7P2WF4KimzpXM/cigX4NvRLsIHGEvfn+S1tPL+ljUdf6b29AmSZqGrTcdZsbp0APScc4Ygdi+Yq73oeMoO47xHzjMH+Lplbk+SIBXWjX1UZMQXDIjIs2WKW9kI7LbkWdnbupCnXhHMOZw7DuvrK7v63D8NI+kkq4hWjPi5QduvIFfnbpuZBX/pbtGXC90jFfSo11YWUydzKuaxpXDPqibQqEj7hSPexDon35HsxisUSzblGZqaGHpAONJa4P//1/LY9AmEl4JKJLBnzmV098W+Eh7kx6JXjYm+cC797h+1fqy7gE5CuckRkQIVSgcZsI/lSPkxaVciQKWXoLHSSC3KYMzzzSMfT1KfqRz3zq4xcMQjH8taly9vtTGSoUrEU+1ftz87MTmqTtaNWbsz3qEzEKJQCEv74/86q8CvY3LmOGck5Y9oC1l/grARcIiPnRYkw/CHcTgucoz1bpLZCsyJMNAqGRWRAOzM7eXzL4yRjSWJejJjF8D0/bM311Jo7GRQHeedaZCJaVLMonHN4lNVVxtnSnCtLMJzwUzTnG2kvtlAdV7dJkemiJZNXMDwBKRgWkQG15lupTFRSl9QF22RVKAZR1meRyac+WU9lvJJcMUcyNnpjh2tSCRpcZtTKG6qEl2Br50aqa8f/d2t/Cbg0jlhkbKXjMba2Zlk0U1NHTTTq0ygiA2rJtZDw1L12MssVSsp8KZOWmbG0dilt+bZRLbciMZQOjqMv7VfRlNtBttQ5rsc98cBZLJ5Z0WvZhsbOPcYWi8joSid8drTnCQL11ppo1DIsIgNqzbdSGdddzMksXwrwy56ZUyYbM3s7cB3gAzc7577eZ/0i4EdAXbTNF51zvx6LuoxFIq1kzCPue5QCV5aENmaGmceOzGYWVh00bsfVOGKR8vA9oxQEdOSLVKfUVXoiUcuwiPSrUCpQCArEPN0zm8zyxUAtwzIkZuYD3wPOAA4Dzjezw/ps9hXgLufc0cB5wPfHqj5JP8n8qvmj2jpsZtSmE2SLe079Nl4qY9Vsy7xGMSiUrQ4iMr5aMvq+TzS6yhWRfmVK5RtPJ6MnXwyIlSFJkExqxwEvO+deBTCzO4F3Amt7bOOArix6tcDmsazQwuqFvNb22ojL2di2kWufuBYIe01k8iWOmHEsR85444jLHirffAICduV2MCe9/7gfv6f+xhEPROOLRYYn6fvsaMuxoL5i3xvLuNEVkoj0K1vMhpe7MqnlS2oZliGbD/SMPBuiZT1dBXzAzBqAXwOfHMsK1SXrqIpXhb+XhmnlvJUsql7U/dw3Y1d+M883PzUaVRyWCr+SLZ3rCFz5Wqj7G0c8EI0vFhm+ioTPttYcTrM8TChqGRaRfnXkOzRv8CRXKgUEzumupwxVf3dP+l69nQ/c6pz7VzM7Afixmb3euT2jOjO7GLgYYNGiRX1XD65CZiytW8qzO58lFUsNq4xVC1exauGq7uelUsDlf/yXYZU1WuJeko58I+2FZmoSM8pSh/7GEQ9E44tFhi/me+RLeTrzJSqTCsEmCr0TItKvlnwLCV+ZpCezknOaVEmGowFY2OP5AvbsBv0/gLcDOOceM7MUMAvY3rcw59xNwE0AK1asGHaTyH4V+7HW1lIMiqOSy8D3PWKeEZS5lSbppVjf9uIewbBvHnPTi0j4ozellIiUmYO2bFHB8AQyLg0GZnaLmW03s+cGWL/KzFrMbHX0c0WPdW83sxfN7GUz++J41FdEwkzSCoYnt0LgUDgsw/AX4GAzO8DMEoQJsu7rs81G4FQAM1sGpIAdY1mpuB/n4LqDaco2jVqZMd8od4/FlF9B4Eo05bb1+mnofJUd2S3lrZyIjKq477GzPVfuakgP49V77laiO8h78Qfn3PLo52oYdEZLERllpaBER6GDuKf0/5NZqeQwDfyWIXLOFYHLgP8EnifMGr3GzK42s3Oizf4J+KiZ/Q24A7jQjcNAuIXVC4l5MQql0cnI6nvl/4aYGelYJRWx6l4/NbEZbMtsJHClMtdQREZLRSLG1hYlKJ1IxqWN3jn3iJktGcaug8loKSKjLFfKgQsv0mTyKqplWIYpmjP4132WXdHj8VrgxPGuV9yPc0j9IazZtYbZ6dkjLs+bwL/jYl6MjmKBtkIztYmZ5a6OiIyCRMyjJZMnWyiRivvlro4wsbJJn2BmfzOz35jZ4dGywWS07GZmF5vZk2b25I4dY9pbS2RKyxQz/afQkUmlFAQoJbhMNftX70/CS5Av5UdclmeGZ+GNo4ko7iXYntlU7mqIyChrzWq+4YliogTDTwGLnXNHAd8F7o2WDyaj5e4Vzt3knFvhnFsxe/bI7xiLTFeZYkYx1BSQLwR4uqshU0zci3PIjENoybWMSnkx3yNXLN/URnuT9itozu8gX9IYQ5Gpwvc0bngimRDBsHOu1TnXHj3+NRA3s1kMLqOliIyy1nwrcV/jhSe7nOYYlilqXuU8kn4yHNIxQnHfyJcm5rhcMw/noCm/R5JuEZmkKhI+21sVDE8UEyKvt5ntB2xzzjkzO44wSG8EmokyWgKbCDNavq98NRWZHlpzyiQ9FeRLAb6C4SF58tUSz27sHRiVO9uw7CnmxTh0xqGs3r6aOZVzRlSW73kkfJ9CyRH3J973pSJWydbO15iTWqA8DiJTQDLmsbMjT65YIhnTuOFyG6+ple4AHgMOMbMGM/sfZnaJmV0SbfIe4LkoK+X1wHku1G9Gy/Gos8h05ZyjLd9GwlMwPNnlCiUFw0P07MYSW5sV/U4G+1XuR0W8glxxZC0sBiyckaYzXxydio2yuJckV+qko9ha7qqIyCgwM3COtuzE/J0z3YxXNunz97H+BuCGAdbtkdFSRMZOPshTdEV8T3crJ7tCyZHwJ8RomEllvzrjw6t23wwqBo4/lbE+0j/f8zl0xqE8vf1pZsdGlidkZmWCdTs6CBxMxPtHvsXYmd1KVby23FURkVHgmdHUkWdWVbLcVZn2JkQ3aRGZOLLFbLmrIKPAOUe+qKkbZGqbWzmXyngl2WKWVCw17HISMZ85NSl2tOWoSU28S6OKWBU7sptYULmUWJnnf9/Q2MnV9+/ZSe/EA2dx6rK5ZaiRyOSTTvhsa81y8Nzqcldl2lOTgYj0kilmcEolPemVojmGJ2Ajl8io8cxjad1S2gptIy5rv5pUNB3ZxOOZj3OOlvyustbjxANnsXhmxR7LNzR28ugrO8tQI5HJKR332dWZp7E9x66OfK+ftmyBYIJO9zYVTbzbnyJSVh2FDnxTa+JkVwwcppsaMg3MrZjLGreGwAV4Nvx7/FWpGDWpONnCxOxRkfLTbM1sZGaqfK2vpy6b22/rb38txSIyMDPDN+PRl/u5iWRhYr+51Unm1qSorYhTlYhpdogxomBYRHppybUoedYUUAzUvi/TQ8JPsKBmAZvbN1Ofqh/y/hvbNnLtE9cCUCgFdOZLxAa46FxWdwxHznjjiOo7XEk/TXN+J5liB+lYZVnqICKjZ0blwOOFS4GjsSPP5uYMDvA9w4uyyZuxz15fXZnnPSPsI2bhfqPF9tHzrDoVY3ZVkup0nKpkjERs4nZGVjAsIr205ltJ+kroMNmVgkCdpGXaWFi9kA2tG4a838p5K3s9j3mGGTj2vNjckd0EzZQtGAbwLMbO7BYWVh1UtjqIyNjzPaMmFYdUmCMgcA7C/+9T963wHv+M5xSBDseujjybWzLgDHBUJGPUVyRIxz0qEjGScY+Y55HwPSqTPrEyJvtUMCwi3YpBkUwhQ0V6zzFhMrmUSjC4P5sik19NoobaZC2ZYoZ0LD3o/VYtXMWqhat6LWvY1cnGXR3Upnv3kPnZq/1OejGuqmLVbO5cR11yFtXxunJXR0TGiTeY5uBu5b8Rnoz5VLM72V++GNDYnqMYOIolB7Y7svfMmFOTZF5tmvrKBJUJ//9n786j5Lqvw85/73uv9qUXoBt7kwQFkZQoSlRAQseiZyAvGWmOJrFjx7biJLYTWzNKnMjOJMPkJMeWlM3M2M7YEyc2x0eWlcXKWI4cjSMviiLK2ghJZChBJAhwAdBAd2Np9FZde713548qAA2gG13VXdXvVdX94DS76r1XVZdAd9W77/f73bujPdUtGTbG3FD1q6jojr4Jmd5oBL6lwmZoiAiH84d54eoLHSXD65nIJTi/UCQgelVGHUje39YAACAASURBVHFJu1nOLH2Th8ePkXC3XkG72zaqMj3srMq2MRD3nA2nSgeBslxqcGllEdVmcbGJXIJswiOT8Eh4DomYS9x1WtPF6ep5qiXDxpgbyo2yDSYOiGpDt1VMyJh+M5GewBEHP/C31Sc9EXPZnU2wVKqTTUTvNCnuJqlpjdcKL/LgyNtwIlDw8J337wasmvTtTs0VODVXuKPStiXIxtzkOEI26ZFtpaW1RsCVQpWZxTLB9bnhzdnWt3x3RXCS2W03X4/eu7wxJjSleslGhQdE1Q9wrfKkGSIxN8Y9+Xu4ULiwpUJaa+0bSTG/WmWpXLuxrdFqdVKs+WTi4SagWS/Pcm2Bi8XXmcoeCTUW2LjK9LD73KnLdyTC56+VgHn7+zJmA3cbRb5OVZvroMXZ9lV/S4aNMTesVFeskvSAqDV8XMuFzZA5kDvA2eWz236efCrGo1NjrG31+YV5DwWSMYfFco2RZJwwrzflY6PMls6R9UYYT06GF4jZ0HoXCWwquTHbJyJdq45tc+iMMTcs15aJu5YMD4JaPbCehGbo5ON5RhOjlOqlbT9XOu6RTdz8ch3Bc4Q37x/hnvEMy+UalYbfhai3RsQh543wWuHblBqrocVhjDH9zEaGjTFAc8rJam2V0aRVKB0ENV9Jxux6pxk+943cx/NXnicd601VfNcRDo2nGU3FOHO5wHK5Ti4VC2V0wXNixII4Z5ZeYDzR3rRbz4mzN33IagoYYwyWDBtjWqp+lUADO0EaAKpK3fdJh7yu0Zgw7E7vxnM8GkEDz+nuac50YZqnvvbUjfuqSqURcDD5CI+Mf0coa4lTXoaKX2a+OtfW8bWggiPC3vRUjyMzxpjos2TYGANApVFBxUpJD4LrhX5skrQZRjEnxr35ezl17dQdyz4ccdiV2rWl5z2279gd20SEq5UZ4q5DKvadLJZqpOIuSW9nk+Kk2347qaSmOb96hlxslEws38OozEY6aUNllaeN6S1Lho0xAFT8CqKWPg2Chq+IpcJmiN03ch+5eO6O7a8svkK1USXhJTp+zuOHjnP80PE7tl8fKX74QJ6lcp3z80UWyzXSMY+Ye+dMm7CX8rviknTTvLJykofHHsdzYuEGNGQ6aUNllaeN6T1Lho0xQLOS9HZ6c5ro8ANFrWG0GWJxN87+7P47thdrRV5feX1LyfBmRISxdJyRgzEWSlWmF0qU641bjgla7UDyyXAT0KSbolBf4vzqKxzOPWQt9XZQJ22orPK0Mb1nybAxQ6Ye1LmwcoFAAwINUJRAAy6XLpNwu3+CaHaer4GNDBuzjvHUOK8svdLT13AcYXc2ye5s8o59lbrPc+cXUMJfxpD1RrhavshIfIzdyX0hR2OMMeGwZNiYITNfmufk/ElSXqrZp611SiYi5GJ3Tis0/afh28iwMevJx/MIgqqGMhqajLnkUzGqdZ9kLNyZOM33/DHOFk6R9nKkvWyo8RhjTBisbKwxQ2ZmdYZ8PM9YcozRxCgjiRFGEiPNk0SbKjcQGn5A+ONOxkRPzI0xkhih4ldCi2FvPhlqf+K1PMfDkxivr7yIr43NH2CMMQOm42RYRDIiYgsLjelDdb/O1dLVnvXfNNFQbQQ4dmHDmHXtzeylVC+F9voj6eZ64SC0CG6V9rKUGqucL5xB1WaUGGOGy6bTpEXEAX4E+FHgMaAKJETkKvAZ4GlV7e0CHGNMVyxWF1FR6yU84GqNADfskrXGRNR4cpygy6no7f2HN3Js3zGOHzrO7myC5XIjlL7E68nHxrhSuUjCTXMgc2/Y4Zg1OmnDtF3WxskMo3bWDH8e+K/APwC+raoBgIiMA+8CfkFEPqWq/653YRpjumF2ddaKZA2BZjIcdhTGRFM2nkUQAg26cmFwvf7D65kuTAPNFk2T+SRXV5fJEI1kWEQYiY1zsXiGpJtiV9ISoijopA3Tdp2aK3BqrsCXX9v661kybfpRO8nw96hqXUTuuZ4IA6jqAvB7wO+JiDWpMybi6kGdS8VLjCXHwg7F9FjVD3BtmrQx6/Icj13JXZQb5a4sGdmo//Dt1o4c5xMeriP4qpH5XXXEJeuN8urKSRJukmxsJOyQhl4nbZi263OnLm8rEbaeyKZfbZoMq2q9dfNTwNvX7hORd6jqs2uOMcZE1FJlqWsjISba6n5AKmbNAozZyN7MXl6cfzG0+gmu67A3l+TSSpV8Mjq/q54TI+VmOL30Am8ef4yka/UlhsV2E2/riWz61aZnxSLyQyLyC0BORB66rXjW070LzRjTTXPFOZsiPQSCQKn7AbZk2JiNjSRGQm8/tjubwNeolNG6KeEmcUR4Zflb1INa2OEYY0xPtXM58stAEvhJ4JeBB0RkCZgFyj2MzRjTJY2gwVxxjpG4TXsbdI0InlybcIlIBqioajT6+URALp7DddxQZ8tkkx4J16XuKzE3Wlev0l6OlfoSJxeexZVbTxU9x+MN+beQcFMhRWeMMd3TzjTpGeDjIvKaqn4ZbhTPug94ucfxGWO6YKm6hB/4uE40irWY3vF9EOsxPNSsC8TmHHGYSE2wXF0mG8+GEoOIsG8kyYWFErFU9Eqv5GOj+EHjjvHzYqPAfGWOA5nDocRljDHd1M40aQG4ngi3bi+o6nOqWlx7jDEmmi4VLxF342GHYXaAH9jIsOHzwP00u0DsVdVDqjoJfCfwLM0uEH85zACjYE96D+VGuBPcxrNx/JCna9+N63h4t31lvTxzpfM0gkbY4RljzLa11VpJRH4P+M+qOn19o4jEgSeAH6P5wfuxnkRojNkWP/CZWZ0hH8+HHYrZAfVAQ18LaUJnXSDaMJIYIexJFOm4RzbuUW0EJLz+KG7oikugPku1q+xO7gs7HGOM2ZZ23nnfDfjA74jIrIi8JCKvA68A7wP+pap+rIcxGmO2Ybm2jK8+nhOdiqWmd/zAEuFhd1sXiFuIyDtuO2ZoZWIZ4k489BHOfSNJyvX+GmVNuVlmi+dQtfcbY0x/a2fNcAX418C/bl1J3g2UVXWp18EZY7bvcvEynlgiPCwafmBrhoeciPwQzVaIORF5CDizpnjW08AjoQUXISLCZHqSq+Wroc6cGcvEiS24LJWblZuTnkvccyNdET7uJliqzbPaWCYXGw07HGOM2bKO5uSoal1V51R1SUTeKSK/1qvAjDHbF2jAzOoMuXgu7FDMDqk0fJwon0WbnfBl4CVgjGYXiFdE5HkR+QOsC8QtJtOTVP1qqDHEPZe3T43yyIFR7tudJRVzWa3UWSzVqDaiWwMg7iS5VJre/EBjjImwjoaLRORtwF8CfgiYBj7Z5uM+CrwXuKKqD6+z/0eBJ1t3V4EPqOo3W/vOAQWaU7Ubqnq0k5iNGWbL1WVqfq25Ns4MhVpDca2m4VCzLhDty8fzRGGJvec65FIOuVSM/aMp/EBZLtV5aW6ZmBfvbORih6TcDAvVK1QaJZJeOuxwjDFmSzZNhkXkjTRbNLwPuEozAf4OVZ3t4HU+Bvwr4OMb7D8L/I+quigi76E5jevYmv3vUtX5Dl7PmLYEGlCqlyjWiwTr9GfV1p8gCPDVJ9CAgIBG0KDu16kH9ebtoL7ttVPXX2sr/w/Auq/vB7ZWeNjUGgFOFM+czY4REdGmW7pAAAu3HxNKgBGS8lIkvST1oE7MiU5NMdcRxrNx9o2muLJcIR/B1ksigiMu85U5DmbvDzscY4zZknbOkl8G/gvwP62tJt0JVf1TEbn3Lvu/subus8DBrbyOGV6FWoF60KwHc/38bqPEMtCA5coy1yrXWKouERAgKhsef71zmCCICILgiNM8EcDBEQdX3G1XJZXWn+u32zkeuOtiB0EsGR4yVd/HFcuGt6qSOEEt+QL/8fWbv4N9mDFaF4g2iQh70nuYK85FcgbNofEU11ar1PyAuBu93+uMl+NSeZq96Sm8CF1MMMaYdrVzlvwDNEeGvygifwL8LvC5NcU4uu2vA3+45r4CfyIiCvyGqj690QNF5P3A+wGmpqZ6FJ6JmkKtwJdmvnRzg17/pjcS2VsouI5L0ksylhzDscTBDJB6Q4nHh3ea9LcWvsKppee3/PhS7rXWrb4e6Xo38NdodoG4D1gCUjQvnf0JzS4QL4QYX6Tsyezh/Mr5sMNYV9x1OTKZ49szy4xl4pErjddssxSwWL3KRGp/2OGYkJ2/VuIjf/BiW8e+8/7dfPdDe3ockTGba6ea9KeAT4lIBvg+4G8Dvy0i/wX4pKr+UbeCEZF30UyGn1iz+Z2qOisik8BnReRlVf3TDWJ9muYUa44ePdqHF/NNp1SVMwtniDmxSF7VN2Yn+YHiB8GOVKHdbtLZKxdLzWT2YHpryaxXP0y88jZ++OHvvLGtESj/lT/oSnw7wbpAdGY0MYrruPiBj+u4YYdzh7FMnH0jKa6uVsgnozf6mnIzzJbOsTu5b/0L0GYovPP+3UB7KxrPXysB85YMm0hoe/6kqhaBfw/8+1Yhjr8I/B9AV5JhEXkE+E3gPap6bc3rzra+XxGRTwGPA+smw2b4XKtcY644x2R6MuxQjAndMxee4XMzX8bbgWx4u0lnrxxM389Do2/nkfHv2NLjf+uZWpcj2nki8jngb6vqi6paF5HHgEdE5E9U9Wthxxc1nuOxL7OPK6UrPb+oOl2Y5qmvPdXWscf2HeP4oeMATO1Kca1Upe4HxCI2XbrZZukahfoS+fhY2OGYkHz3Q3vaTm7bHT02ZidsaTFhqxDHb7S+tk1EpoD/BPwVVT2zZnsGcFS10Lr9Z4GPdOM1Tf/zA5+X5l8iF8/Z1WhjgBOXTrBQm2UyeaDnr7XdpNP01EFVfRFARL4D+LfAfwQ+JiL/sDXjy6yxP7ufi4WLPX2NY/uObX5Qy3ShudT7ejIc91yOTGR5cXYlktOlE06SC8VXeCh21JYeGWP6yo5U1hGR3wGOA7tF5CLw80AMQFV/Hfg5YBfNKV1ws4XSHppTtK/H+h+6OS3b9Le54hyFesFGhY25TmE8vp8fPvzTYUdiwrWy5vZfBX5dVZ9sLTf6NGDJ8G12Yqr08UPHbyS3m1lv9HgsE2cyn2ChWIvcdOmUl2GpNs985RKTtnbYGNNHdiQZVtX3bbL/J4GfXGf768BbexWX6V91v87L115mNDEadijGRIZ1yjEtr4rID9JcUvR9wF+AG8uNEqFGFlE7OVV6q0SE+3ZnWFit0Qh0R5ZDdCLrjXBh9Qyj8V3EXfsxM8b0h3b6DP+du+1X1V/uXjjGtOfc8jnqWmfEjeZJizFhsFTYtPwszanRvwN89nr7wlYxrWyYgUXZTkyV3q6453LvRIbXrq4yloqHHc4tPCeG+nCh+Br3598UdjjGGNOWdkaGc63vDwCP0ZxiBfC/YIWsTAhK9RKvLr3KWNIKdRizVqDbbndtBoCqXgK+V0QcVQ3W7HoXzf7CZh1Rryp93WQuyexSmUrDJ+lFK86sl2e+MsNEcp8V0zLG9IV2Wit9GKDVY/jtqlpo3f8QzZ7DxuyoM4tncB030icrxnQiCBRflT+9+AW+dunEusdo6z/KzRu3jwTPFS8wnrD1eqbptkQYVf0Tmn2GzTo8x2N/Zj+XS5cjO1UawHWEN0xm+daFZRKeG6kLYCJCys1wtnCKh8cfx5UdWY1njDFb1sm71BSwtudEDbi3q9EYs4nl6jIXCxetaJZpyzMXnuHE3PrJZRhUm0lvw1cagaKq6Jqk9lLldQD2Jg9v6fnH4vt5aOTPdClaY4bPvuw+LhQuhB3GpkZSzWJai6U6uUS0Es6Em2Kpdo3LpYvsz9wbdjjGGHNXnbyD/lvga61evwp8P/DbPYnKmA1cK1/DczxrpWTacmLuBNOFaaZyU1193qCVxLbLD5S6H9AImg8SAUcEEWFtDRxrV2RMuPplqjTA1HiG+dVFfFXciH0m5mKjXCy+xnhikqSXDjscY4zZUFvJsDQzj48Dfwh8Z2vzT6jqf+9VYMas52r5KikvFXYYpo9M5aZ48vEnu/JcNd/n8nKViwslgo7KVQlJzyEec7EOnGantCpH/wDNWVw3Pu9V9SNtPPbdwK8ALvCbqvoL6xzzQ8CHaF4g/6aq/qWuBB6ifpkqDZCKu9w7nubcQpHRiBXTcsXFE49zqy8zkTyAKy6OuLiOh4u7hQvasuaW0Hy4IDjNC4s4dpHcGLMlbSXDqqoi8vuq+meA53sckzHr8gOfxcqiFc4yO67uB1xZqTC9UCJQyCW9yI3EGLOO/wwsA88B1XYfJCIu8GvA9wIXga+LyKdV9aU1xxwB/gHwTlVdbPUwHgj9MlUaYO9IkrmVCjU/IO5G61JbJpZntb7MSn2xlco2/6so0sG1RAW48X6rCNJ8jtY+VUVEkA1XTzf3iDjNRJq7HbtDRLgv+yAjiV3hxmGM6Wia9LMi8piqfr1n0RhzF6v1VQINcCRaH/im/5RrPjXfB2iu2dW1Baq0eYLVOrZWD7iwWMQPlFwihhux3p7G3MVBVX33Fh73OPCqqr4OICKfAP488NKaY34K+DVVXYRmD+PtBhsV/TRV2nUdDu/O8OLsCumEe2PU9MZ3aRa1CutTMxvbudH1jfus643Cg3rz4J0IaUMNrfN64UUejr2DmBOtUX1jhk0nyfC7gP9VRM4DRZqX+FRVH+lJZMbcZrW2atOgTFe8cqXASqWO0xphgJuT8G6/JwiZhIdnSbDpP18Rkbeo6skOH3cAWDs0ehE4dtsxbwQQkS/TnEr9IVX9oy1HGiGe43Ege4BLxUuRnyoNMJaJc2hXimLFJ1C98eX7iq/Q8P3WOGqTqpJNxIi5g/WetvH5wTrjwCH/r7t4rNSXmC2e5Z7cA+EGY8yQ6yQZfk/PojCmDVfLV0m4ibDDMH1OVSlWG4yk4rZ+1wy6J4AfF5GzNKdJt3sRe71U4fahNA84AhwHDgJfFJGHVXXpjicTeT/wfoCpqe4Ws+uVvZm9vLb0Go2g0Rplbf6VOOKQi+ciNUNJRLh3V/auxwTBzSR5pVLn5bkC2YRHLGJTq4dJzstzqTzNWGLSejIbE6K2k2FVPd/LQIy5G1VlvjxPJpYJOxTT5+p+QKBqibAZBlu9iH0ROLTm/kFgdp1jnlXVOnBWRE7TTI7vWEqlqk8DTwMcPXo03PmpbRpPjnN0z1F89WkEDRQlCAJWaitcLV9lV6q/1no6juC0rnHszrq8eb/DS3PLpONe5NYaDwsRh5Sb5fXCSzw8dgzPiVaLLGOGRUe/eSIyRvPDLnl9m6r+abeDMuZ25UaZml/riylrJtpqjb44Fzdm27ZxEfvrwBERuQ+YAX4EuL1S9O8D7wM+JiK7aU6bfn2rsUaNIw4Hcgfu2F6ql7h84fKO1K+YLkzz1NeeumP7sX3HOH7o+LaeeywT5+EDI7w4s0IQU5JetNdGD6qEm2S5tsBs6SxT2SNhh2PMUGo7GRaRnwQ+SPMK8QvAO4CvAt/Vm9CMuWm1vhp2CGZA1PyA0BeMGbNDROSt3GyJ+EVV/eZmj1HVhoj8NPDHNNcDf1RVXxSRjwDfUNVPt/b9WRF5CfCBv6eq13rzfxEd6ViaqfwUs6uzPe1scGzf7Uu0m6YL0wDbToYBRlJxHjk4wsmZZVQhFbOEOAy52CizpXOMJyZ3tOCYMaapk5HhDwKP0ZwW9S4ReRD4cG/CMuZWC5UFYm4s7DDMAKjWfUuFzVAQkQ/SrPr8n1qb/p2IPK2q//dmj1XVzwCfuW3bz625rcDfaX0NlXvz93J++fyNlj69cPzQ8XUT3vVGircjm4zxloOjvDS7zGqtQTZuU3V3miMOKTfD6ysv8ebxx3DF/g2M2Umd/MZVVLUiIohIQlVfFhErgWd2xJXSFVJeKuwwzAAo1hp4tkbODIe/DhxT1SKAiDxFc0bXpsmw2Vg2nmVfdh+LlUXyiXzY4WxbNuHxyMFRXruyymKpNpCVpqMu6aZYri9wtvAyKTdzo2ibg4MrHuPJSRyxkXtjeqGTZPiiiIzSXCf0WRFZ5M6CGsZ0Xc2vsVpbZXdqd9ihmAh75sIznJg7ccu26cI0U7lbq9eWa76d6JlhITSnMF/nY2sEuuLwyGG+XPwyefo/GQZIxlzetD/P1ZUqr11dpeII2YRnPyw7KOeNslK9xjLzzX73rV7Ida1xhEeYSO0POUJjBlMn1aS/v3XzQyLyeWAE+MOeRGXMGqv11VtaW5jhtl7SC3B68TQAD4zdnLAylZu6Y+1dseaTsamAZjj8FnBCRD5FMwn+PuCj4YY0GEaTo+xK7mK1tko2fve2Rv1CRJgcSZJPxzg7X2S+UCWT8HBu++wVwfqu94AjDpnYnRdX6kGNmeLr7ErusdFhY3qgkwJanwN+SVU/o6pfaG17mlbvQGN6ZamyZImwueHE3Il1R3wfGHtg0yqrdT/ADwLsPM4MA1X9ZRF5BngnzWT4x1T1hXCjGhxvGHsDJ+ZODEwyfF0y5vLg3hzzmTgzS2X0thbT5ZpP3HVIWsGtHRFz4hQbKyxW59mV3BN2OF1z/lqJj/zBizvyWu+8fzff/dDg/N2Z7upkeOQ+4EkReUxVrxfOOtqDmIy5xdXyVVsvbG4xlZviycef7PhxVknaDAMR+ZKqPiEiBUBZ80MvIqqqgzG3N2S7krvIxXOUG+WB+4wSESbySSbyyTv2XS1UOHO5YMnwDkq7OS4WX2UsMdHzll474Z337wbmd+S1Ts0VODVX4Muvdf/1LMkeDJ0kw0vAdwO/KiL/H/CXexOSMTf5gc9iZbGnLSzM8Kg1AsD6DJvBpqpPtL7nwo5lkIkIbxx7I89dfm5Hk+GN+g+3a7t9ikfSMQQhAPo/LesPcTfBUu0aS9V5xpOTYYezbd/90J4dSyI/d+pyTxLhTpNsS5yjq5NkWFS1AfwNEflx4EuAZSimp4qNIqo6EFdCTfiqdX/zg4wZECLylKo+udk2s3UTqQnSXppqo0rCS/T89TbqP9yubvQpjrsu45kYKxWfTNxGh3dKys1wsfgao4nddk7UgV4l3p0k2eevlYB5S4YjqpNk+Nev31DVj4nISeBvdj8kY24qVAs2q9V0Tanm4zl2EmGGxvcCtye+71lnm9ki13E5MnaEb179JpNe70fsNuo/3K5u9SmezKe4VlwGLBneKQk3yXLtGiv1RUbju8IOZ+h1kmTv1NposzWdVJP+DREZA44A1xeRfKwXQRlz3dXyVRJu76+2m+FQrPl41lbJDDgR+QDwN4DDIvKtNbtywJfDiWpw7c3s5ZXFV3ZsdDgK8slmlelAsYKEOyjpprlYfI2R2LgVFjWmSzqpJv2TwAeBg8ALwDuArwLf1ZvQzLBTVebL82RimbBDMQOiXGtY0RczDP4DzdaH/xz4+2u2F1R1IZyQBpfneDw4/iDPX35+R0aHo8BzHSZyCa6t1sgmrFXdTkm4KZZq8xTqi+Tj42GHY8xA6GS+4AeBx4Dzqvou4FHgak+iMgYoN8rU/TqeYx+0ZvsafkDdD3DtaroZcKq6rKrnVPV9qnp+zZclwj2yJ7OHfCJPqV4KO5QdM5FLUA+CsMMYOkk3zYXia6haMUhjuqGTLKOiqhURQUQSqvqyiDzQs8jM0Futr97R39CYrWq2VTJmeIjIbwMfVNWl1v0x4JdU9a+FG9ngccThoV0P8ezcs6Rj6bDD2RHZRAzPcfBV7SLjDkq6aRZr88xX54g5d07LdxBAEBGu/6FH/z6C4IiD4OCIIDh4Tqwnr2VMr3SSDF8UkVHg94HPisgiMNubsMwwUVWK9eIdie/V0lVirr2pmu5otlUyZqg8cj0RBlDVRRF5NMyABtmu5C4mUhOs1FbIxwe/lbPrCHtyCS6tVMknbQbXTsq4Wc6unLpjuwAqzSRVVRERFG0mxNuw3ii0QCvJbr4CqiBwMH0/+zP3buv1jNlJnRTQ+v7WzQ+JyOeBEZprkozZlkvFSzx3+Tlc59a1nEEQWH9h0zW1hrVVMkPHEZExVV0EEJFxOrsIbjogIjw4/iBfmvkSuVgusgWO1utTvNXew7uzCWaWy12KzLQr7iaJu8nND9xhgfqt9k+7SHvW5tz0h04KaCWAHwDuXfO4twEf6X5YZljU/TovXnuR0eSoVY02PVWsWlslM3R+CfiqiPxu6/5fBP5ZiPEMvJHECAeyB7hSuhLJi7nr9SneTu/hTMIj7rrUfSVmlfqHniMuMSfOucJpHhx9u/VDNn2hkyvE/xlYBp4Dqr0Jxwybs8tnqQd1RtyRsEMxA65sbZXMkFHVj4vIN7jZ9eEvqOpLYcY0DI6MHWG2OEugQeSSgfX6FG+n97DjCHvzCWaWyrasyQCQ9rIs1eaZr8wymToYdjjGbKqTZPigqr67Z5GYobNaW+XVpVcZT1p7gH73zIVnODF3Ykdea7owzVRuquPHFWs+CS9aJ6bG9FJrRtfbgDzNz/sfFBFU1WZ09VAmluG+/H2cXznPrtSusMPpufFsgunF4amibTaX80Y5v3qGfHycpDscBeVM/+okGf6KiLxFVU9u5YVE5KPAe4ErqvrwOvsF+BXgfwZKwI+r6vOtfT8G/KPWof9EVX97KzGY6FBVTi2cIu7G71grbHbedpPZ04unAXhgrPcF5qdyU+tO9bsb3w+o+T7puP2smaFiM7pCct/IfcyszjBfnr9jX9JNko1nQ4iqNzJxl1TMpe4HxFy74GjAdTycwGW6cIYjI2+N7Pp5Y6CNZFhETgLaOvYnROR1mh+qAqiqPtLma30M+FfAxzfY/x7gSOvrGPBvgGOtgh8/DxxtxfGciHz6ekEQ05+ulK5wuXiZPZk9YYdigBNzJ7Y84grNJHirBVh2Qs3ffjVNY/qQzegKSdJL8sSBJ6gH9Vs6JZTqJZ6//PxAJcMiwr6RFGfni4ymLBk2TVkvz2LtKovVq4wnJ8MOx5gNtTMy/N5uvJCq/qmI3HuXQ/488HFt1m9/VkRG4ITtyAAAIABJREFURWQfcBz4rKouAIjIZ4F3A7/TjbjMzqsHdV6cf5GRhK0TjpKp3BRPPv5k2GH0RM23StJmKG1rRpfZnqSXJMmtFX+zsSxxN04jaOA5g1PYe3cuzsximUrDJ+nZDBzTlPHynC2cIhcfWbcnsjFRsOk7saqe34lAgAPAhTX3L7a2bbTd9KnzK+ep+BVyCSu7b3ZGrRHc0cfamCHwBNub0WW6zBGHfZl9zBZnGU2Mhh1O18RdlzfuzXLy4jJx18WxiTgGiDlxKn6J11ZeIuPdOhvCEZfdyf0kItgiygyXKF2WXO+tU++y/c4nEHk/8H6AqamtTfc0vVWsFzmzcMaKZpkdVao1cK2tkhk+7wk7AHOnvZm9nF/ZqXGG9qzXe3gjGy2JGUnFmdqVZnqhxFgq3uUITb/KeiOUGwWK9eVbtjdoUKgv8saRRyNXdd0MlyglwxeBQ2vuHwRmW9uP37b9mfWeQFWfBp4GOHr0qA0DRdCri6/iOZ4VzTI7qljzidlQhRk+P7bBdqsmHaLRxCiu4+IHfiQ+CzspSLhZT+IDo2mWSw1Wqw2yiSidYpqwiAhpb/2ZgEu1a8yVpjmQuXdngzJmjSi9U30a+GkR+QTNAlrLqjonIn8M/DMRud69/s8C/yCsIM3WVRoVZlZnhqLVhImWctXHsyqnZvgU19xO0qwBciqkWEyL67jsy+zjSulKJGpnrNd7eCObjR67jvCGySwvTC9S95WY9XY3d5GPjXKh+Ar5+Ci52OAsGzD9pe1kuNX66EeBw6r6ERGZAvaq6tfafPzv0Bzh3S0iF2lWiI4BqOqvA5+h2VbpVZqtlX6itW9BRP4x8PXWU33kejEt018uFS8hIjYdxuwoP1AqjYCRWPgjMMbsJFX9pbX3ReQXaV54NiHbn93PTGEm7DB6IhV3ObI3y6nZAmOZuNXxNxtyxCXjZnl1+Vs8PH7MimyZUHQyMvyvgQD4LppTrArA7wGPtfNgVX3fJvsV+Jsb7Pso8NEOYjURE2jA68uvk4/nww7FDJm6HwBqJ2TGQBo4HHYQBkYSI4gIgQYDeYF4VybBvtEGl1cqZBMejggi6xeBMcMt7iap1qucK5zmDfm3WE9is+M6SYaPqerbReS/A6jqoohYhQTTloXKAuVGmVzcKkibnVVrBGGHYEwoROQkNwtOusAEtl44EmJOjD3pPSxWFwfyc1FEuGdXmlrDp1zz8VVp+EGbNf3XJkPa2iJr7vd/sqQoMdclE7cZS9DsSXyteol8ZYw9qUObP8CYLuokGa6LiEvrnUlEJmiOFBuzqXPL50h5qbDDMEOo5tvblBla711zuwFcVtVGWMGYW+3P7me2ODuQyTBAzHV40/5b10T7gRKo0pwM2B7V5onn9Ye0m1JHWeArr14tsFKpk0/Gwg4ndCJC3hvjfOEMSTdN0k3jiIsrLo7YBQPTW50kw78KfArYIyL/FPhB4B/1JCozUEr1EldKV9id2h12KGYIlWr+QE5DNGYjIvJvVfWvAN+nqr8SdjxmfWPJMRycgZ0qvR7XEdwBGNnthjfvH+H0pVWWy3XyqdjQ/624jkfSTXF66YVmQ/TWdhHBFQ9p/elHq3UXQbhSnmU0vou4a2ujo6STZHgS+D+BR2jOUfk+VbWqlGZTs8VZHHFsHYgJRanWsLZKZtj8GRG5B/hrIvJxbptXakUooyHuxtmd3s1qbZVsPBt2OGaHxT2Xh/blePXKKvPFKqMpKzaWcFMk3FtnEaoqAcHNqQFr9+1UYNsk+IByrtBMm0YS40wmD5KLjeE5UWrsM5w6+RfIA78OLACfaH035q4aQYOzS2cj0T7CDKdirWFtlcyw+XXgj2gWy3qOOxdhWhGtiDiYPcgLV18giyXDw8hzHY7syeHNO8wtlRlNx7Frt7cSEVzcvl4qLhIAwkh8HFWlXC/ySvWbiDi4Es1kOObEibtJEk6SuJMk4SYjMINFWn9nLg4OIg6Ibjuotv8FVPXDwIdF5BHgh4EviMhFVf2e7QZhBtd8eZ5aULMrXyYUQaBUawH5lK05MsNDVX8V+FUR+Teq+oGw4zEbG0uOoa01tDZ7aji5jnD/RIa4J1xYKHF71qcombhH3C7qDgQRIeVlSJFBNUAjOL6tQKA+1UaJkhbwtdEane/kGXpABNHmd229jJPU9HafdisZyhXgEnCN5tRpYzZ0duks2Zhd8Ta9t1yusVSq3bIt0GaxFTvFNMPIEuHoS3pJdqV2UW6USce2fU5n+pSIMDWeYW8+ece+lUqdl+cKxNPWwGXQiDiRPT9x+6VwWRfy7raTYRH5AM0R4Qngk8BPqepL2w/BDKqV2goL1QUm03bNxPTehYUyS6UarnPr1fOU1ydv6MaYoXQge4CTV09aMmyIr/N5tSvjMJ6pUqg0yCZslp0x3dbJb9U9wM+o6gu9CsYMlpnCjE2PjqBnLjzDibkTt2ybLkwzlZsKKaLta/gBy+UaI+k4NpHMGNNPdqV24Tke8+X5W7YHQUA2nrUkeciJCPfuzvD89CKBYmuKjemyTtYM//1eBmL6Q6ABVb9KtVGl4lco1osUagUqjQqNoLmmoO7XCTSg7JeZTNmocFjWS3oBTi+eBuCBsQdubJvKTXFs37Edi63birUGCpYIG2P6TspLcfzQ8eaavDUWK4s8d/m5yCXD04VpnvraU3dsP7bvGMcPHd/5gIZAOu4xNZbmwmKJ0ZRNlzammzZNhkXkS6r6hIgUuHVmtgCqqvmeRWcipRE0ODF3gpXqCioKCq7jEnfiuI6LIw4eHrFYDEccRhixgiAhOjF3Yt0R3wfGHhi4k5aVcsN6VxrTss7n9Y1d2Od2JMXc2B3bJtOTJN0kdb++7v4wbHTRdLowDTBQnytRs380xaWVCjU/sGJafejSkvJbz9Q2P7ADb5lyOXrYloJt16bJsKo+0fqe6304JsouFC6wXF1mIj0RdiimTVO5KZ58/Mmww+i5a6tVknH7QDAG7PN6UDjicN/IfZxePM3u1O6wwwGaye56Ce96I8WmuzzX4f6JLC/NrjCesdHhfvKWKRfwu/qc568q5682ODm9vee1hLqzAlpPqeqTm20zg6ncKHN64TRjybGwQzHmFrWGT7HWsKljxqxDRMaAI8CNMrWq+qfhRWQ6sS+7j1MLpwg0iECPTxO28UycsUycYs0nYxeA+8bRw91POL/xur/tRLiThHqQk+ZOqht9L3B74vuedbaZAXRm8QwiYgWxTOSsVrt7tdWYQSEiPwl8EDgIvAC8A/gq8F1hxmXal/JSHMgeYL48z0hiJOxwTMhEhPsmMvz384ukYq4V0xpi3Uiw202o75Y0D0KS3M6a4Q8AfwM4LCLfWrMrB3ylV4GZ6FisLHKxcJGJlE2PNtGzWKrhOTZiYsw6Pgg8Bjyrqu8SkQeBD4cck+nQVH6KmdWZsMMwEZGJexwcS3FhoYzbhWxYbysvIEhrm+A6gitCJx+xcc+1YpZ9ot2EeqOkudOp2lFNnNsZ5vsPwB8C/xxYW1G6oKoLPYnKREagAd+e/zaZWMaKYZnIUVWurdZIxqL35mpMBFRUtSIiiEhCVV8WkQc2f5iJkrHEGJlYhmqjSsJLhB2OiYCp8QwT+eTmB7ZB1+bCCr4GNHyl7gdU6j7VRvN+O/xAWSnXbNnSgNkoae5kqvZGiXMUEuR2CmgtA8vA+25feyQitvZowM2szrBSW2EybS2STPRU6gE139ZOGbOBiyIyCvw+8FkRWQRmQ47JdEhEODxymG/Pf5sJL7oztDZquRSmQeuccJ3jCJl49JatVes+3zi/0BpXNoOuk6na6yXOUZl+3UkBLVt7NGSqfpVT104xlrCiWSaaVqt1+8A1ZgOq+v2tmx8Skc8DI8AfhRiS2aK9mb28OP9iZAtpRbFP/enF05xePM2JuRNhh3KHQU3SEzGXfDJGteGT9OwitblpvcR5o5HlS0sK+NFLhrG1R0Pn1aVXCTSITH9DY263UKwRd+0D15j1iMjPAr+rqhdV9Qthx2O2Lu7GOZQ/xOzqbCS7OmzUcilMz1x4JpKJ8KD3ZN6TT/LKlYIlw2ZTG40s/9YztXX7MvdqtLiTZNjWHg2RQq3AuaVz7E5Ho7ehMbfzA2WhWCObsIs1xmwgD/yxiCwAnwA+qaqXQ47JbNGh3CHOr5wPO4y+EcUEHQa/J/NouvmZbFOlzVat15e5l6PFnSTDtvZoiFwuXcZ13EhOxzIGoFxrEKhaawljNqCqHwY+LCKPAD8MfEFELqrq94QcmtmCfDzPSGKEcqNMykuFHY4x64p7LvlUjGrdt+KWZkvWGzG+fZS4m9pOhm3t0fBQVaZXpsnH82GHYsyGVioNu+pstmW99UqXlpS9owP3k3UFuARcA6waYp8SEe4fuZ/nLz9vybCJtL35JGcuFywZNn1hS6XobO3RYFuprVBpVMjFc2GHMtS2u95pujDNVG6qixFFy7XVKgn7oDXbcHLavyP53TsqrSla/U9EPkBzRHgC+CTwU6r6UrhRme2YTE8ynhpnubrMSGIk7HCMWddIyqZKm/6xaTIsIgXu/Hm+fl9V1YYPB8yl4iVcJ5ong1EtiNELpxdPA/DA2NaW5k/lpiJZ4bMbGn7ASqXOiPUyNG24W8XKvaPCTxwf2J+je4CfUdUXwg7EdIfruLx14q18ceaL1nfYRFbccxlNxSnXfVJ20dpEXDt9hm14cIgEGnChcCGyo8In5k4M/IjndQ+MPTCw7Re2q1hr2BVns66NehkC3DNx60/MII0Cr0dV/37YMZjuS8fSPDrxKF+79DUm3Amr7WEiaTKf4MzlgiXDJvI66TP8c+ttV9WPdC8cE7bl6jI1vxbp6VdTuSmefPzJsMMwIVou1XEtFR5qG432rpf43jMhPWvJEEUi8iVVfWLNzK4bu7AZXQNhMjPJG8feyCtLrzCZtmXgJnqaU6XFLlybyOtkzXBxze0k8F7gVHfDMWG7VLyE52xpKbkxHQsCpREE1BrN76qbPwbg6mqVVHw4EhvT2WjvsCW+61HVJ1rftzzFR0TeDfwK4AK/qaq/sMFxPwj8LvCYqn5jq69nOnf/6P0sVhdZqi4xmhgNOxxjbhH3XMbSMUpV3z6vTaR1Uk36l9beF5FfBD7d9YhMaPzA52LhYmSnSJudpapMLxQp14NtP8+NHLf1VL4qlXpAzQ8Qbu5vMxfGQW4U6DCDpd3E15LezYnIzwL/r6rOdPg4F/g14HuBi8DXReTTtxffEpEc8LeB4SjkEDGu4/LIxCN86eKXqDQqJL1k2CEZc4vJfIKXLxVIYe/TJrq2MwSYBg53KxATvqXqEvWgbiPDBoCVSp0LC+WutEaQ2+4IQsJzSMVtsvMw2GhK83os8e2qPPAnIrIAfAL4pKpebuNxjwOvqurrACLyCeDPA7dXov7HwL8A/m73QjadSHkp3r7n7Xx17qsU60U8xyPmxPAcD8/xbD1xRE0Xpnnqa0+1dWw/1w7Jp2IIzevg9pNooqqTNcMnuTlw49Js1WDrhQfIXHGOuDuwVVVNB1SVc/MlkjHXil+YdW03wd2IJb7do6ofBj4sIo/QbLH0BRG5qKrfs8lDDwAX1ty/CNxSml5EHgUOqeofiIglwyHaldrFO/a9g9XaKsVGkXK9TKlRYrWyio+PaPP3TkURbc7F2ZXaZYlySDrp8jBdmAbo22Q47rqMZeIUKz5pmyptIqqTIcD3rrndAC6raqPL8ZiQNIIGM6szjMSjWzjL7Jylcp1Cpc5Y2i6ODKpOktn1WILbV64Al4BrQDvVltb7R72xikFEHOBfAj/ezouLyPuB9wNMTQ1+J4Aw7E7tZndq9x3b/cBHUVSVgIBAA84tn+P8ynl2pXaFEKk5fuh428ltu6PHUbY3l+LbhWWc299VBBKezQ4z4etkzfD5XgZiwrVUXcIP/Mj2FzY7JwiU8/NFK3jRh3o1WrseS3CjT0Q+QHNEeAL4JPBTt6/73cBF4NCa+weB2TX3c8DDwDMiArAX+LSI/Ln1imip6tPA0wBHjx5ttzSA6YL1PtMPjx5mujBNPagTc6z2gumtfMpj30iSeuPW+iPlhk+p5pOxcw0Tsk6mSR8F/iFwT+tx11s0PNLm4+9amVJE/iXwrtbdNDCpqqOtfT5wsrVvWlX/XLtxm/bMFGZIuImww7jhmQvPcGLuzposw9JjOEyLpRqr1YaNCvehk9M+l5aUvaM2WjvspJmlHgV+RlVf6PDhXweOiMh9wAzwI8Bfur5TVZeBG8OQIvIM8HetmnR/SLgJHhp7iJPXTlpbJtNznutwZM+dhVmvFiqcuVwAK65lQtbJNOl/D/w9mklpR+Vl26lMqao/u+b4vwU8uuYpyqr6tk5e07SvHtSZK84xlhwLO5QbTsydWDfxncpNdbTexnTGD5Rz14qk41ZErV/tHRV+4rhdyBh2qqoi8ugWEmFUtSEiPw38Mc0z1Y+q6osi8hHgG6pqnST63IHcAc6unKXcKJPyUmGHY4ZQKmbnGSYaOvlJvLqND8B2K1Ne9z7g57f4WuYu6n4dX2+dRrlYWSTQIHLFNKZyUzz5+JNhhzFUFopVynWfsZQlU8YMgK+KyGOq+vVOH6iqnwE+c9u2n9vg2ONbC8+ExXVc3rz7zTw796wlwyYUqZiDICjrFykwZqd0kgz/vIj8JvA5oHp9o6r+pzYeu2llyutE5B7gPuC/rdmcFJFv0Czc9Quq+vsbPNaKdNxFpVHhixe/SCO4te5ZQEA2lg0pKhMVfqCcv1YiY6PCxgyKdwH/m4icA4p0uLzJDLZdyV1MpiZZqa6QT+TDDscMGdd1SMdd6n5A3I3WYIwZLp2c9f4E8CAQ4+Y0aQXaSYbvWpnyNj9Csxfi2uHLKVWdFZHDwH8TkZOq+todT2hFOu5qsbJIXetMpCfCDsVE0LVClUrDRoWNGSDvCTsAE10iwoO7HuRLF78UydlhZvCNZmLMLVUtGTah6iQZfquqvmWLr7NZZcq1fgT4m2s3qOps6/vrrUIdjwJ3JMPm7uaKc6Rcmw417Kp1n7p/67J/VTi3UCQbt8qixgyQH9tg+0d2NAoTWfl4nntH7mV6ZdpaLZkdl0/GmdFK2GGYIddJMvysiLypzbYMt7trZcrrROQBYAz46pptY0BJVasisht4J/AvthDDUGsEDS6XLjOeHA87FBOi1UqDb88uEaxTAs9xhJhrK3dMeFQVX320rRqNvZ38E6gSaLNHa933QejHoYvimttJ4L3AqZBiMRF1/+j9XChcsFZLZselYlZJ2oSvk2T4CeDHROQszTXDba896qAy5fuAT6jq2rOch4DfEJEAcGiuGd5KQj7UlqvLqKpNgxpiq5U6J2eWibsOyYR9AA2LelCj5BdbZUqiRVUABZHm9ASBuCRwnVgbBVV6d+FGxCHueLjiEnPiqLoElWC1Zy/YI6r6S2vvi8gvAlYJ2twi4SZ40/ib+Ob8N5lITdh5gtkxCc/BEQgUHLsWb0LSSTL87u28UDuVKVX1Q+s87ivAVqdnm5ar5at4jhVGGlarlTonLy4TjzkkPUuEB51qQMkvUg/qJNwk92SOkIjoEgnX8fAkhufE8CRGsz1utNT9AK1rdfMjIy8NHA47CBM9h/KHKDVKvLL0CpOpyUj+Hg6r6cI0T33tqbaOPbbvGMcPHe9tQF3kOMJIMka57pO0UWITkrazI1U938tATO+oKjOFGbJxqxg9jArlOt+esUT4dn7QICAgUJ9Agxu317p1kkr0+UECgJVGkV2JPUymDpDx8jbSM6RE5CQ355O7wAS2Xths4MjYESp+hdnVWXandocdjqGZ3Lbr9OJpTi+e5sTciR5GdHdbScZH0jGWr9UtGTahaTsZFpGN+gvaB2vEFeoFqn7VWicMIUuE17faWEGAuJMk7qbwJEbMieM58dZUrZujItL60w8S7lUE4dFdR4k5ibDDMeF775rbDeCyqjY2OtgMN0cc3rzrzVQaFRbKC4ynrMZI2I4fOt52cvnMhWdCTYSnC9MAHSfDmYTXVpUIY3qlk3mzVoijTy2UFwZ6ZKhc81ku16j5iu8H1AOlEQT467273jbSp9wc/VMFH4WguT3Q60f0r1ojIBV3LRFeox5UQeEtu94xcAlj3F0BGLj/L9MZEXkMuHB9RpeI/FXgB4DzIvIhVV0INUATWZ7j8ejkozw79yzL1WVGEiNhh2Ta1Eni3AvtTuW+XTru0u/nWqa/dTJN2gpx9KmZ1RnSsXTYYfSE7wecvrTCarWB6zQLMYgIbuv7RtbbJYCLg7itccEuDAaGPaKYitOXJXB7RTVgtVHgwZFHLWE0g+w3gO8BEJH/AfgF4G8BbwOeBn4wvNBM1MXdOEf3HOUrs19hpbZC3Lm197yIkHDt/dN0R9xzibkufqC4VkXLhGA7FZWsEEcfqDQqLFWXmEhNhB1KT1xcKlOsNRhLxzc/2Ay9QmOZPclDjCZsPZwZaO6a0d8fBp5W1d8Dfk9EXggxLtMn0rE0j+97nFPXThHordOsivUidb9udUhM14ykYiyX62TiNovN7LxO1gxbIY4+tFRdwsEZyMqQK+U6FxZKjKQsETabq/plYk6CQ9n7ww7FmF5zRcRrrQ/+buD9a/ZZWwHTlnw8v24BpyulK3zj0jcsGTZdM5LyuLZaoZleGLOzNv1QFJE3AHu4sxDH/cBMj+IyXTK7OkvCi8Z0pk6KO0wXppnKTW24v+4HvHK5QCruWm86s6mg1WrozWOP4TmxsMMxptd+B/iCiMwDZeCLcOPzfDnMwEz/G0+O4zkejaBhLRtNV2Tinq0aNqFpZznh/wUUVPX8mq8ZoNTaZyKqETS4UrpCJpYJOxQATsyduFFtcDNTuam7thSYXihRbQRWGMq0ZaW+yMH0YXKx0bBDMabnVPWfAv878DHgCb3ZI8yhuXbYmC3zHI9DuUMUaoWwQzEDItmaHm0JsQlDO5f07lXVb92+UVW/ISL3dj0i0zXL1WVUNVKVpKdyUzz5+JPbeo7FYo3ZpTKjtk7Y3KbmVwhu+zhtBDUyXo59mXtCisqYnaeqz66z7UwYsZjBsz+7n7PLZ8MOwwyImOuQins0/ICYG51zVjMc2kmGk3fZl+pWIKb75svzuM5gjZzWGj6vXCmQTXhWJdncolhfwXU8Ut6t69iELAcyh3HFpvMZY0w35ON5MrEMlUaFpHe300QzTKYL0223WDq279gtraBGUzGuFqqWDJsd187Z4ddF5KdU9f9Zu1FE/jrwXG/CMtulqsyszgxcgYvz10r4gZKJ25uluclXH58Gbxp5jKQ3mG3EjDEmKkSE+0bu48X5Fy0ZNgB3Xdp2u+tL5tYmw/lUjLnlcrfDMmZT7STDPwN8SkR+lJvJ71EgDnx/rwIz7VNVtDU19PrSsNX6KuVGmVw8F2ZoXVWt+1wuVBi16tHmNoX6MlPZN1gibIwxO2QyPcm3+TaqOpAdK0xnjh86fktyezfrjR6n4i5gP0dm522aDKvqZeA7RORdwMOtzf9FVf9bTyMzbWkEDU7MnWC5unzjPUS0eSM2YFVzF0s1BHurNLcqN4pkvCx7UgfDDsUYY4ZG0kuyJ72H5dryQF14N+FIei4OENBedV9juqXtRXSq+nng8z2MxWzBTGGGleoKE+mJsEPpuUvLFVIxW/dpbgo0oBqUOTLyCI4M1vp4Y4yJuqn8FF+/9HVLhs22uY6QTXrUGr51CjE7yjKLPlb1q7y8+DIjyZGwQ7nDej2FN+sdfDelWoPVWoMxmyJt1ijUl9iXvpdMLB92KMYYM3TGk+PEnJj1HDZdMZKKMbNUIWk/SmYH2Y9bHzu/fB5VjeR06Os9hdcmv5v1Dr6bhdUajk2QNmvU/CoxJ8H+9L1hh2KMMUPJdVym8lOcWznHeHI87HBMn8slY9T9EkvlOgI36+EA0toiN+43C7mlYq5VoDbbYslwnyrVS7y69GqkP3y60VMYmkXB5pYrpOP242qaVJWiX+DBkbfjRfBikDHGDIt92X28uvRq2GGYAZBPxXjroeZsx1Y92GY6vPZ264ailGo+VwoVVsvNmjIJzyURc23NsemIZRd96pXFV/Acb+D6CK9ntdKg6vuk44P//xo1ftCg7Bfv2H5r9fLWvV4N3N/4JHRAFEEI1GciuZ/RxK4evagxxph25GI5cvEc5UaZlJcKOxzTJzrpSbyZQJVGoNQbAY1AN3/AOpojzc3R5l6czjw0+nYeGf+OHjyz2S5LhvvQcnWZC6sXmExNhh3KjphfreKKXecLQ6GxxJ7UFDHnzrXajjg4OCCCK25rClNvMmJHBMHBEQcRB0FIeZmevJYxxpj2Xe85/MKVF0i6SWuzZDa11SVzG3FEiLtC3HXoKBVWJdBmMh2o4gfNr0Dp7Hk2sVCbxV9QS4YjypLhPqOqvLzwMikvNRQfOL4fcKlQIZOwH9WdVvOrJN00U9k3WKVmY4wxGzqQPcBSZYnzK+eZTE8OxfmJ2bpOehKHKQgUVSXg+ky4DY7T5rRupZlI355J/8oLv0ix2uhprGbrLMPoM9cq17havsqe9J6wQ9kRK9UGfqC49sG640r+Kkfy1rLIGGPM3Tni8Obdb0YQzhXOMZGawLEZXabPOU5zxtt2z4I8R3AE6r4Sc+18NmosGe4jgQa8NP8Sudjw9PO7slIh7loyttOqfoWUm2E0sTvsUIwxxvQBRxzetPtNiCOcXTrLRNoSYmOuu1ad45Pn/hXOEA/uRHXdtCXDfeRy8TKFeoHJdO/XCq/XJ7gT2+kpfF3N95lf/f/bu/MoudKzzvPf597YMiI3Zaak0lIpqVSbqlymqhCFoQB7sKENbWymYRqzTJsBjhu6zXpmxjDMMR73mT4GunuaoTkNbto0+DCYtenqboMBQ8HBpkRV2eVaLNemklSSUmsq18hY7r3P/HEjVaERmyYvAAAgAElEQVRUppRLbJn5+5TDGXHjxo0nb17Fjee+7/u8VQY1t3DHVeJ57hr8Cn2R6QGfOX6Bz756eVXrnrpS5sBosc0RiYgsL7CAIyNHCAh4depVJcQipGOka1HCQj0m2Ka58Jnyq5wpv8rxqc+v6/UzQ2nf89890fodqGR4k4iTmC9Pfpmh3FBH3m+5eYLXYiNzCi+aLtcXawhLB1XjBYqZAYZUqXlN1pK0rsXxiVkAjuy5dY+QA6NFHj2s1nwR6Z7AAu4duRfDeHkqnfli0c3GXQJkggzZIEsmyFy7iWx2b7v9bTw4+rV86dwMQ33bczrIZyc/t+5EuN30KbNJXCxfpByVO9IqvKhV8wSv1/mZCoWMukh32kI8z73DD2+Jq/ntSlCXs5akdS2O7Bng0cNjvP3I9qgTICKbn5lxz8g9jPaNEnsM3DoRjj1mob7AfH2e+Wie+fo8taSG+QotQcYbhYoWV/Elz7WxFc5vUm+4eXIex7lhsh6HUq6kqai2kUI2vOkxs9W9eeRrN9RF+jcerwHwXQ9d31v0L/jMhuICJcObQqdbhTvJ3bk6X6MSJUuWw8xCnSF1ke6oSrxAKTvEYHak26G0xGdfvdyxrsNKWkVE3mBm7Czu3NA24iReNoG4tsyb5r3HSTzB3a/dTzy54bWdtNIFgEpc4akLT5EP81viwrPcWi4MCMxIUI/HXqNkeBM4P3+ecr3MrtLWmld4vhZx4tI8U+XastWiC9mwnRd1ZRmVeJ4jA1+5pabFODBa5EPvur/bYYiIyBqFwdbtHXbn0J28NvMaY30a2rIdBIHRn89QjxLyGaXDvUTJcI+LkihtFS5snVbhepxwbmqB1yfL5DIhI0W1/vaChWiewewIA9kd3Q5FRERkSzu84zAT8xMsRAvqLr1N9OczXJitKhnuMUqGe9z5+fNU4gqD+cFuh7Jhi12iX7k0RxQ7Q325bVtVr5tqcZWFZA48wKzRxawxtupw/5u2VKuwiIhIL8oGWR7Y+QBPnHuCQljQuXcbGOjLcm56odthyBJKhntYlES8OPkiQ/n2tQqvNIVSK6ZGapYkzqnJec5MLtBfyFDK6apYNySeMB/NcPfwgxTCItb4D4OAkFyY73aIIiIi28JY3xjjg+NMzE0w0rc1anXIygpqEe5J+qv0sIn5CapxlXwbE5TFKZSWasXUSIvqccJLF2Y5e3WB4VKOXKjDrltm61PsLx1mJL+LYqafvkyJQqZIISwqERYREemwe0buIbCAalztdijSZvlsSFtLnMu6qGW4R3WiVXhRO6dQqtRjvjwxw0ItZriY00dAF5WjWfqzg+wtHex2KCIiIgLkwzxvGnsTT194ml3FXeouvYVlw4BcGBAlTkbjBHtGx5rozOydZvaimb1iZj+9zPPfb2aXzOyZxu2Hmp57n5m93Li9r1Mxd4K7M1WZ4vLCZS4vXOZS+RIXyxd5bfo1anGNXLh5i0vNVSKePTNFLU4Y7MsqEe6iKKkTecQdA/cT2NatzikiIrLZ3Fa6jT39e7i8cJm52ty123x9nnK93O3wpIUG+9KK0tI7OtIybGYh8CvANwFngCfN7DF3/9KSVX/X3T+w5LUjwM8BR0nL/DzdeO3VDoTedlPVKT537nMEBLh5Orl8Y7L44cJwt8O7TpI45VqMu5M05vVLPJ0T2N1J3IkTJ4qdKEk4O7VAIRNSyCr56iZ3Zzaa5s7BByhk2j/froiIiKyemXHf6H3kghxxEl9bnpAwXZ1mrjZHf66/ixFKqwwUslyZq9GHvhv3ik51k34EeMXdTwCY2SeB9wBLk+Hl/APgz919svHaPwfeCfxOm2LtqDOzZ8iFOYbzvZX4Luf0ZJnXr5YbcwKn5Yd9sQxxIzlulGPCAqOUy5IN1R7cbbPRNLsL+xnN7+52KCIiIrKMvkwfD+x84IblF8sXeer8U0qGt4i+XNj47iy9olPJ8D7g9abHZ4DlqjN9h5l9A/AS8JPu/voKr9233JuY2fuB9wOMj7euEnK71OIaZ2fPsqOv9+d1nVmoc+ZqmeFNNB1S4gms8gPnhrXcm5Z7+p/7tfs338biut0Xe0QuyHF7/50ahyQiIrLJ7CjsILCAOIkJA7UmbnaFjIpo9ZpOJcPL/dWXZgv/Ffgdd6+a2Q8Dvwl84ypfmy50/xjwMYCjR4/2RjZyE5fLl3GcwHq7unI9Tnj5wix9ubAnE+HEE2bqV5uSvbSlOrCQYI3D4q1xuC3+xIzAAgICgiAksACz4I3nl3l9+l+6Ti/kn7cVx8kE2W6HISIiImuUDbLsH9jP+fnzHSmqKu2VzwQYkKApfXpFp5LhM8DtTY/3A+eaV3D3K00P/wPw802vfduS1z7e8gg7zN05MXOCUq7U7VBu6fRkmWqUMNTXmwnVbP0qe4uH2FnYkybAliatvX6RQURERORW9vbvXXYaTNl8gsAo5UOiONFUoz2iU3+FJ4G7zOyQmeWA9wKPNa9gZnuaHr4bON64/2ngm81sh5ntAL65sWxTm63PMl2dpi/T1+1QbmqqXOPc1AIDPZoIz0ez9Od2sK90kEImnSs3E2SUCIuIiMiWMJwfJhfkqCf1bociLTBYyFJTReme0ZGMwd0j4AOkSexx4Pfc/QUz+4iZvbux2o+Z2Qtm9kXgx4Dvb7x2EvgXpAn1k8BHFotpbWYTcxNkgt6e5rkWx7x0YZb+fKYnu3JESZ3YI+4YOKLpgkRERGRLCizgwMABZqoz3Q5FWqC/L0uU9Pxozm2jY9mYu38K+NSSZR9quv8zwM+s8NqPAx9va4AdFCURp2ZOMZgb7HYoN3X68gJx7JRyvZcKL04XdNfgmymEmi5IREREtq7b+m/j5amXux2GtEAhDFhtgVd5w/kp5zcer7V8u73dNLlFXVm4QpREPd0yPDlX5fzMAsPFXLdDWdZsNM2uwj5G8ru6HYqIiIhIW/Vn++nP9VOJKhQyhW6HIxuQ78FGpl73wHgIxLdcbz16Nxvbwk7OnKSYbW9r5uOvP86xiWO3XO/07GnGB66fhmqhFvNio3t0DxRDvkElXiAb5Bjvv0vTBYmIiMiWZ2YcHDzIC1deUDK8yeXCkGwYEidO2IvTtPSgo3eEHL3jxiGRn/u/N75tXZrosPn6PFcWrlDMtDcZPjZxbFWVB8cHxvnqPW9M+RzFCS+enyEMArI9WOUu9phKXOauwQc0XZCIiIhsGzuLO0k8wV1dbDe7gUJILVYRrV6gluEOm5ifaMxV2/4rQeMD43zwkQ+uen1357XL85Rrcc9OozQXTTPefyelbG+Pt5b2+czxC3z21curWvfUlTIHRjWmXERENr++TB9jfWOUozKlbO9PzSkrGyxkmZqv05dVAdhu672mvy0sTmJOTp9kMN+bidz5mQrnZyoM9mgiXE9qZCzLzsL+bociXfTZVy9z6kp5VeseGC3y6OGxNkckIiLSGeMD48zX57sdhmxQMZchURGtnqCW4Q66Wr1KNa4ylB/qdig3mF6o8erFOYb6sj05ThhgPprjjoEjPV14TDrjwGiRD73r/m6HIbJlmdk7gV8CQuDX3f2jS57/KeCHgAi4BPyAu5/qeKAi28xY3xghIYknBKY2rc2qoBbhnqF/RR10dvYshbD3ih5U6jHHJ2Yo5TOEPVqQqhZXyYcFRgu7ux2KiMiWZmYh8CvAtwD3Ad9tZvctWe0LwFF3fzPwB8AvdDZKke0pG2bZO7CXycok5XqZhWiBalSlHteJkkjjiTeJXCbAMLUN9wA1sXVIPakzMT/BjsKObocCpOODa1FCJYo5dblMYEauBwtmLSrHc9w1+GYC05U0EZE2ewR4xd1PAJjZJ4H3AF9aXMHd/6pp/SeA7+tohCLb2KGhQ8RJTOQRSZIQeUTkEfWoTi1J52F192v1aZbev5nAAsIgJLCAjGWuPc5YRjN4tFAYGAOFLFMLtVX3yDQgAQzDgCAwQjOyoRGGgVo410nJcIdMVaa63qVloRZzZa7KzEKdmWr6AQpGGBr9ud49FCrxAqXMAMN5jf0UEemAfcDrTY/PAF+9wroAPwj8SVsjEpFrBnIDPLT7oWWfc/c0MY7r134mnuA47n7dzxtei1OP69TiGtW4SjWpUo3S20w8k77GSbOyxZ9L9GX6VNxrle65rZ9avPq24SRx4sSJ3ImihFocU6knLNRi5ip1kusudKTtzs1/ruZ77pBe21g+Fb+WrZgRWDq1l5Em8Yu3rXJppHczoC3m3Nw58mG+a+/v7rx8YZaZSlq5rpTLsFmmNqvE8xwZ/kqNjRER6Yzlzg7LfmMzs+8DjgJvXXFjZu8H3g8wPj6+0moi0gJmRtayZFs8/aS7EyUR9aR+7bZUnMR84eIXyASZrn7n3SxymZBWtUW5O/U4oRY59SRh8bpF+rORALO4zHFfuZeAA4mnyXfiizca20+oRgnz1RhvpNsBRj4bkM+EmzJBVjLcAb3QRXq2EjFTqbOjmOtaDOuxEM0zmBthINsb3ctFRLaBM8DtTY/3A+eWrmRm7wB+Fniru1dX2pi7fwz4GMDRo0c1RE5kEzIzsmGWbHjzJPuhXQ/x5IUn2dm3U40YHWRmLU2ubyW9OOLU4oTZhTqXZqtML9RwIBeG9GXDTdPopmS4A3qhi/TZqTK5zOYab+vuVJMF7iw9oHEqIiKd8yRwl5kdAs4C7wW+p3kFM3sI+DXgne5+sfMhikgv2l3azT3D9/DS1ZfYVdrV7XCkTawxVjkbBpRyGW4b6qMWxcxVYy7PVrkyXyV2JxsEFHu8N6qS4Q7odhfp+VrElbkawz3cKpx4csOycjTLSP42+rO9NxWViMhW5e6RmX0A+DTp1Eofd/cXzOwjwFPu/hjwi0A/8PuNi5Wn3f3dXQtaRHrG4R2Hma5NM1mZ7JnCsdJ+uUzISCZkpJQjjkvMViMuz9W4NFshdie0gL5sSDbsrcxYyXCb9UIX6YmpCpkw6Nl+/DP1KQywJS3nYZBlX+lQd4ISEdnG3P1TwKeWLPtQ0/13dDwoEdkUAgt4YOcDfO7s5yjXyxSzxW6HJB0WhgHDxRzDxRyHxkrMVetMztWYLNeYX4hxIBuk44wzYXeLcSkZbrNud5Gu1GMuzCww2Nd7rcLuzkx0leHsKHcM3k+mxcUeZPP7zPELfPbVy9ctO3WlzIFRnVhFRER6VT7M8/Duh/nbs3+bjjXWd7xtKwyMob4cQ305DgHVesx8LWa6XGNyvsZ8LW5aO614nQ1DSrnODO9UMtxmrewi/fjrj3Ns4tiq1j09e5rxgXEuzFQIsJ6be8w9Ybo+yVhhH4cG7tH8wV22XNLZC45PzAJwZM/AtWUHRos8eljTbImIiPSyofwQX7HzK3jm4jOEwfXf8xynlCmp1XgbymdD8tm0O/WhnWnV6sgT4hiiOCFKnFNX5plZqDPY1/6LKEqG26jVXaSPTRy7luTeyvjAOEd3P8K5qwuUCr31Z048ZqZ+lT3Fg+wvHVa1wR7w2Vcv92SL65E9Azx6eIy3H9nd7VBERERkjfb172MoP3RDbZhaXOPpC08TWkg+o2mYtrMgMHKEaYWK9P/oL2R4+cIsk+UaQ325tjbq9VaWtMW0o4v0+MA4H3zkg6ta99zUAq9dniPsoUrMcRIxE01xoP8ubus7oCrRPeTAaJEPvev+bochIiIiW4SZMZAbWPa5o7uP8sTEE4wEI+pGLdfJhgH33DbIySvznLu6wHAx17aK1GqSa6NuVpGO44QzV8uUcr3z4RInETP1q9wxcD97igeVCIuIiIhsU2PFMR7c9SCTC5PESXzrF8i2EgbGHWMl7thZYqpcox63Z5p6JcNtsthFuj/X35X3vzJfoxYnPVO+fDERPjz4Jnb17e12OCIiIiLSZfsH9nPv6L1cXriMe3uSHdm8zIx9O4rct3eQmUq9Le+hbtJtMl2dbnsV6Wo95vJclellDo7phTqlXG/8eWOPmYmucsfg/exUIiwiIiIiDYeHDlONqpyaOcXO4s5uhyM9aLQ/TyEbEidO2OL+0r2RLW1i7k4lrtxwNevM7Jl1d5FeqWr06dnT3D4wztVyjYnpBSbnawQYucyNcwgXMiG5sPsN/3GjWNahgSPs6tvX7XC2lbVUiO7F4lkiIiKy9ZkZ947cSyWuMDE3cUPlaVrRYGyQC3Pkghy5MKfirZtQMRdSjeIbj48NUjK8QadnTvP8ledZOl10QsLOvvVd3VquanTizu6+fdyWfRMvnJsmF4YM9+W6Okn1rSxWjT7Yfw+7+27vdjjbzloqRGu6IhEREemWMAh58843Mz4wjjey38WGJm9BNlyNq8xUZ5ipzaQFbkmubdvc3ri/Qj2bgIAwCAktJAxCMkGGcA3TghqmWjkb1JcLKddaP7ZcyfAGVOMqx68eZ6QwQiZo7a5crBpdjxMuzlQ4PVnGHYq5TNfGAbs7s9E0kNxyXYDYEw70381txVtPBSXtoQrRIiIishlkg2xHukm7O7WkRjWukiQJscfEHpN4ej9JbvyeG3vMQrRANapSiStU4grVqLrq94w8opApMJgbbOWvsq0UsyHn44TF6ZdaRcnwBpyYOgFOyxNhSP+hnp9e4NRkmThOKOWzZNpVU3xV8SRM1yfZVdjPjvzqPqgCCxnMtWaOZRERERGRjTIz8mG+ozO+zNZmefbSs1wsX2S0MNryrr7bQT4b0po+89dTMrxOs7VZTkyfYKxvY11Lz00tcGm2ct2yuWpE4s6rl+Yo5bJku1wIK/GEmfoke4oH2V86rHEWS6xlbG4naRywiIiISPcN5AZ4y563cHLmJC9Ovkhfpq9rM85sVrk29YxVMrwO7s5Lky+RD/MbSgzLtYjXLs/Rl82wdBhBYMZwX26DkW5cWgBrkttLd7O3eKDr4x16MfE8PjELwJE9y08q3y0aByyyPHenGiVU6jFR4ksKIDY+48zbcQFaRES2qTAIOTx8mLG+MZ699CyXypfIhRv7rm8Y6f/suvpFG/2+bhiBBQQWYGYEBNdts5XvtVrZ8MaCwa2gZHgdJiuTnJ8/v6FxDe7OycvzZIKAfOb6hLpXhtdHScRclFaC7pUCWGspCtUpR/YM8OjhMd5+ZHe3QxER0s/X2J0kgThJ70dxQj1OAMMMBgoZ9u8oUsqHFLIhmdDIhQHZMCAM0nXSLwOdO9GLiMjWN5Qf4mv2fg2vz75OOSpveHueOI6TkOCJXysOthGxx0RJRD2pE8fp/cTfKDq2KCG5duHYsLQIWSNBb6wMxhvLl4t/mSvPlr4IxwksLV4WeEjivrjJllEyvEaJJ7xw5QX6c/1r+oK0dLqkepxQrsXLjgO+VDnLzkJ3pyGKkojZaIo7Bx9grLCnq7EspaJQIu2RuJMkq2sObV7L29SCeqsKou5QixJqcZKu640TsDu5TEA2k15szGZC+nMZdpRylPIZSrmQTA9MPSciIttTJshwaOhQt8PYMHcn8eSN4mONn0srgt/s9ctJSIiTNAmvxlWqcZVyvUxsl7hSmaUQZukLSy35HZQMr9HE3AQztRl2F9fWCtg8XZK7s1CPV5w0emdhH0eGH25FuOs2F81waODenkuERWTt6nGybMJajWKqUdI4GaWtoflMcMOwjZVc102qkVu2uhPTzWLJhMZIKc9QX45iLqSQCylkQrKhprAQERFpNzNLp5siJEu27e9XntvLxbmr1LjK5cr5ljQRKxleg3pc5/jkcXbk11cheXG6pNNX5nn9arknxgQvpxZXyIcFdhb2di2GlcYG91oXaZFeN7NQJyFtKW0WYIyUcoyUcvQXMhRzGYrZkKCLVetFREREVjJcKDBTHuK24k72l+4kqdqG+5krGV6DkzMnqcd1hvJD695GuRZx+mqZoUJvJsIA5XiOuwcfJFjDZOKtttLYYBWFElmbShTztYfH2DnQuSkkRERERFptsC/TqP9BWsQ4sQ0PkO5YMmxm7wR+iXSm5F93948uef6ngB8CIuAS8APufqrxXAw811j1tLu/u1NxL7paucpLky8x2je6oe2cvDxPNgjo1caXhWiewdwIw/nuJ5waGyyyMVGSkA0DRkq9e/FNREREZDXSuYZbqyPJsJmFwK8A3wScAZ40s8fc/UtNq30BOOruZTP7EeAXgO9qPLfg7g92ItblVOMqT194moH8wIYmya7HCVfma4wUe/OLqbtTTRa4q/RmjbcT2QJmFiIOjBZXrE8gIiIislnkM+GKVanXq1PlNB8BXnH3E+5eAz4JvKd5BXf/K3df7Pf9BLC/Q7HdVOIJz19+njiJ6cv0rXs7DlTqMf353u2ZPhfPMFbYSyk72O1QRKQF6nHCvuH1f26JiIiI9Ip8JsCttVNYdCoZ3ge83vT4TGPZSn4Q+JOmxwUze8rMnjCzb1/pRWb2/sZ6T126dGljETecnD7JxNwEI30jG9pOnCQkDrkenc4j8ZgkidlX2vxl3kUknXKomAsZLra/uqOIiIhIu+UzAYEZSQvndOxUM+Vy7dnL/hZm9n3AUeCtTYvH3f2cmd0B/KWZPefur96wQfePAR8DOHr06Ib30tXKVY5fOb7hccIA9dhXPV1JN8xFM+wtHqQQqlKzyFYwU6lz720DGvIgIiIiW4KZUcqlRbTymdaMH+5UM+UZ4Pamx/uBc0tXMrN3AD8LvNvdq4vL3f1c4+cJ4HHgoXYGC+k44S9c+AID+QEywcauGcRxQj1KCHv0S2mU1AkI2V28/dYri8imkLhz21Ch22GIiIiItMxAIUM92nwtw08Cd5nZIeAs8F7ge5pXMLOHgF8D3unuF5uW7wDK7l41szHgUdLiWm3j7jx/+XnqSZ2B/MCGtzdTiZZvBu+wKImYi6Ywu/4aiHvCoYEjZIPeLOwlImuzUIsZ6ssyUFAXaREREdk6+vMZLsxUb73iKnUkGXb3yMw+AHyadGqlj7v7C2b2EeApd38M+EWgH/j9Rre+xSmUjgC/ZmYJaUv2R5dUoW65c3PnOD93np3Fnet6/eOvP86xiWPXHpdrEZO1c+wq3GyYdPvNRVMcHDjCUHbJ+GeDfND+IjufOX6Bz756eVXrLjfHsIiszly1zlfsH+52GCIiIiItNdCXJU42X8sw7v4p4FNLln2o6f47Vnjd54AH2hvdG6pxlReuvMCOwo51j7U7NnGM07OnGR8Yx92px86uwj6ODD/c4mhXbz6aZSg3xq7Cvq6NIfzsq5dXneQeGC3y6OHuz3Usstm4Ow7sGlQXaREREdla8pmgpZMr9e48P13y4uSLuDvZcGPdC8cHxvngIx9kcq7Gl85Ps6Ove12QoyQi9oiDA/d0vZjOgdEiH3rX/V2NQWQrm6/F7Oov0Jdr/cT0IiIiIt2UzwTQwumVlAw3maxM8vrs6+zsW1/36OWcn10gH3b3S+lsNMUdA/d1tFL0cl2i1fVZpP3KtYj79my81oGIiIhIrylkQ1o4s1LHqkn3vCiJeO7Sc/Rn+1vWelqLYq7O1yl0sYVmPpplODfKWGFPR993sUt0M3V9FmmvxB0Dxgby3Q5FREREpOWyYUAmDFo2blgtww2nZ05TrpcZK7YuWZteqAPetSsO8WL36P57CWxtUayl2NVyFluB1SVapHPmKhF7d/S1bO49ERERkV4zUEjnGm4FJcPAfH2eFydfZLjQ2uqr52cqFLr4pXQ2muLQwBEKmbV3TV5LsavlqBVYetnVco0oac2H6Lo5GIbjmKU/ccPMAQP8jW5Aq+2t4nBwtNSmgEVERES6rz+f4eJsa6ZX2vbJsLtz/MpxsmGWTNC63ZG4M71QZ7jNhbMST5itT91QVS0hYTA3wlhh77q3rZZd2YqmF2oMFrLcfVt/V+MwDDMIzAgMzJY8bnp+LSM3sqFGv4iIiMjWNVDIcPbqQku2te2T4QvlC1yYv8Cu0q6WbjeK07F77azdXE9qzEfT7CveyUBu6Ibni5n+W3aPXqk7tIpdyVZUjWLi2HlofJhSftt//ImIiIhsOqV8hqRFVbS29bfBKIk4fuU4Q/kbE8mNqsUJhWz7ukgvRPPUvMbdgw+xo7D+6tcrdYdWN2fZahJ3psp1vvrQiBJhERERkU0qnwmxFjU5butvhGdnz7IQLdBfvHV3ycdff5xjE8duWO7uLL0ucWb2dYaye9o2Xni2Pk02yPKm4a+imNn4FCrqDi3bweR8jTt2ltgz3NftUERERERkndK5hluzrW2bDNfiGi9eXX3RrGMTxzg9e5rxgfFry+LEma9FN8x1NZTdw92DD7UyXCAdHzxTv8qO3BiHBo+QDTR9ishqzFUiSvmQI3sGux2KiIiIiGxAIRtyY3Pk+mzbZPjU9Clij8kG2VW/ZnxgnA8+8kEg/XL93NkpcmHQ1u7Qi6rxAuV4nn3FQ+wrHSIwTZ0ishpRnLBQj3jrHbtUXEpERERkkwsDW5xGcsPtw9syGS7Xy7wy/Qo78jvW9fq5Sp3nzkyTywZtnzoprRZ9lXxY5P4dX8VAtrXTP4lsFYk7UZxeJfSmaYmmF+o8ePswQ32rv/AlIiIiIr1rIJ8BC5QMr8eJ6RMEBITB2hPZ2YU6z5/tTCJciReoxPPsLR5iT/FgS6d+EtlK6nHClbkag8UMwbUpidLpee/c1a/K6CIiIiJbSH8hA8aGu/xtu+xqtjbLqelTjBXXXik5SrzliXCURMxHM9iSiUTdEwphift3PEJ/du3VrleaMmkpTaEkm109TrgyX+XowRFuH9GxLCIiIrLVDRaytKKK1rZLhl+afIl8Jn/T+XeXVo52d07Pvs5wdg/5bJhWMGsBb3SBPjBwL6UlVaHNjGKmn9DW9ydaacqkpTSFkmxm1xLhA0qERURERLaLvlyYJmkbtK2S4cnKJOfL59nZd/N5eRcrR+/vv516nFCtJwxn93Df8Fe2LBEGmImm2FM8wG19t9/QMtwKmjJJtrLFRPirDoywX619KlEAABSTSURBVImwiIiIyLaR5mRKhlfN3fnylS9TzBRvmXgm7uwq7ONtoz+EA/35DOHGx2dfZz6apT8zyP7+w21JhEW2snqcMKlEWERERGRbymfCtJvtBm2bZHi+Ps9UdYqdxZVbhd2dy7NV5ioRAP2FLC3OgQGoxVXcncODb1pTN+jVjgMGjQWWjYuShOlynThpzTxut2IGzvWjPwwDc3ADe6M3jANfdXCEfTt0jIuIiIhsN/lMoG7SazFZmbxpC2wtinnt8jwXZ6sEgWHQlkQ49phyPMuR4aPkw75l11kp6T0+MQvAkT0DNzy3lMYCy3rFiXN1voqZcXhXP/35zn1MBIERGASWVoQOzTCzawmyWZogh6F1NC4RERER6R1BYLgnahlerYn5CYqZ61uRFgtlRXFCuR6Dp5M4X66cZWdhX8tjcHdm6pMc6L+HwdzKcxyvVPzqyJ4BHj08xtuP7G55bCJx4lwtVwHjrt0DHBwrUci2d/owEREREZF18STe6Ca2RTJci2tMViYZLYxet/yJiWOcmjnNjuwewiBtiQLYWdjHkeGHWxrDUydinjlZJRMM0xfOgb2w4rqLibCKX0mrVaOY2UqdxJu7IxvgYMadu/q5Y6xfSbCIiIiI9LY4qm90E9siGZ6qTuH4dd2k48RZqEXsyO7hu+/80Y3P2HwLz5yscWkm5NBo8ZZTYqmLs7RSnDgzlTr1OKGUC7l/7xD9+Qxmb3RJDszIZwMlwSIiIiKyKXhcr210G9siGT4/f558kL/2OEmcE5fmqMdOJrC2J8Jz0QyB5Tk02s/Pfdub2vxu289CLaYabbiXxJo4aTH35oJON6zjzWt3RlqAypoep8f4+EiR/TuKDBezql4uIiIiIsI2SIYTTzg/f56BXFp0KkmcE5fnuTBTIdOOClmkXaKfOx033j8GclyZCTkwqiSkVcq1iPlqjOMM92W5faR4qwb3lgoCCCwgtMWiT8u/++IhZvZGN/xOJKOL75AJjB2lHNmw3Zd8REREREQ2ly2fDM9UZ4iTmL89+7c8MXGMSj2mFiVkAuNSmwplPXc65vyUs2sobREsZvrpHw3U9XmD0gJPNdyd4WKOr9jfz9hAnpKqCouIiIiIyBpt+SzicuUygQUcayqWtdgi3I5CWYt2Dzn/+OuqHNlxlGKmvy3vsV24O9OVOvUo4d49g+zf0Ucxt+UPXRERERERaaMtn1GcnT1LKVeiGsUtL5ZVT2rMRzOALSnOVcDMuHf4YSXCG7RQi5mp1Nk73Md9ewc1t6yISAeY2TuBXwJC4Nfd/aNLns8DvwV8JXAF+C53P9npOEVERDZiS2cW5XqZcr1MIRymUk9aViwr8YS5aJqAkDsG7meksIvmLf9p9jgApexgC95t60rcqccJ9chJ8Gt1phbLTdWimGI+5GvvHGVnf16Fn0REOsDMQuBXgG8CzgBPmtlj7v6lptV+ELjq7nea2XuBnwe+q/PRioiIrN+WToavVq6SuPPqxTk2mkc9dSLmuVMxCTHuTi4cJBcUMLsKXL1u3VOT6TzBkorihEo9oRKl+84w3JzAjFIuw3ApSzYwrKmgWYAxUMiwf0cfGRV/EhHppEeAV9z9BICZfRJ4D9CcDL8H+HDj/h8A/87MzN07Vz5fRERkg7ZsMnxy5iQ//lc/zkK9Ti2Cq7Vz6y6W5e588VSNC1PG3h0h+UyRwFZO0LbCPMHuTpSkLbdRnP5MPJ2qZzXMuNbEm8+GjJRyjJRKDBQy5DMh+UxAPhOotVdEpPfsA15venwG+OqV1nH3yMymgVHg8tKNmdn7gfcDjI+PtyNeERGRddmyyXAlqlCNa9QiCINgTcWyrk2N5E5MgrtzZSbk4GgfH/62N2/ZBM7dma/FlGsRBhRzGUr5kGI+QykXUsxl1jQdVTYMKOZD8pmwfUGLiEirLfdBv/RK6GrWSRe6fwz4GMDRo0fVciwiIj1jyybD+TDPN+7+XnI2TCm3fDLWPB9ws1OX0nP1/tGYXJgnG+QZHEunRtrMiXCSOPEyPdjqccJ8LcIddvUXuH/vAKP9eSWxIiLb0xng9qbH+4FzK6xzxswywBAw2ZnwREREWqNjyfBGKlOa2c+QFuuIgR9z90/f6v1iTyjXYMdAmtAtl/guJr0Hdho4JB6T4Nw+FvCWO4b5tgfuIBvkN/Jrt12SXF98CtK77lCJYqpRDJ72WQ7DgPwy42/z2YC7dg2zc6BA3woXDkREZNt4ErjLzA4BZ4H3At+zZJ3HgPcBfwd8J/CXGi8sIiKbTUeS4Y1UpjSz+0hPxPcDe4G/MLO73f3GJt0mtcj59FP9mNWAJYlvw4ExOHJ7wpEDCwDszO9hrG8vpczgTccEr8diq2ycOEljPG6SpI+Xkya0nnZEc7tuDK7bYvJrhAHXCkwt9mA2DAtgrD/PaClHfyFDKZehkNUYXRERubnGGOAPAJ8mvYD9cXd/wcw+Ajzl7o8B/xH4hJm9Qtoi/N7uRSwiIrI+nWoZXndlysbyT7p7FXitceJ9hPRq9IrcIUqSa4/3jsCde+rcvb+SPo+TsQzFzBBDwV6GsqNkghzVKlQqteU32khIDQNLk9WVc0uj+SJ5JgzIhUY2DOjLZshl01baXCYgXGYcbmBGJjTCwAjNCBo/w9DIBOnybBAQrGEMr4iIyGq4+6eATy1Z9qGm+xXgf+p0XCIiIq3UqWR4I5Up9wFPLHntsmWhmytWYtSPffjbTwDXSiAfA/fYI088SedIWmVp5M4ZY5lKnD1OMXeGYu4MxdwZmzHme7odwFbw9NNPz5nZi92OY4024/GqmDtDMXeGYu6MzRjzhs/NnUqGN1KZcl0VK83sqbgcH11LkN1mZk+5u2JuM8XcGYq5MxRzZ5jZU92OYYt4cTP+7RVz+ynmzlDMnaGYO6MV5+bWDoxd2VoqU7KkMuVqXisiIiIiIiKyap1Khq9VpjSzHGmhjceWrLNYmRKur0z5GPBeM8s3KlveBfx9h+IWERERERGRLagj3aQ3Upmysd7vkRbbioB/fqtK0g0fa8fv0maKuTMUc2co5s5QzJ2xGWPuRZtxPyrmzlDMnaGYO0Mxd8aGYzZNCygiIiIiIiLbTae6SYuIiIiIiIj0DCXDIiIiIiIisu1suWTYzN5pZi+a2Stm9tPdjmc5Zna7mf2VmR03sxfM7Mcbyz9sZmfN7JnG7Vu7HWszMztpZs81YnuqsWzEzP7czF5u/NzR7TgXmdk9TfvyGTObMbOf6MX9bGYfN7OLZvZ807Jl962l/t/GMf6smT3cQzH/opl9uRHXfzaz4cbyg2a20LTPf7WHYl7xeDCzn2ns5xfN7B/0UMy/2xTvSTN7prG8V/bzSp9xPXtM3yTmnj6mNwudm9tH5+a2xqpzc/di1rm59THr3Lwcd98yN9LiXK8CdwA54IvAfd2Oa5k49wAPN+4PAC8B9wEfBv7Xbsd3k7hPAmNLlv0C8NON+z8N/Hy347zJsXEeONCL+xn4BuBh4Plb7VvgW4E/IZ2D+y3AsR6K+ZuBTOP+zzfFfLB5vR7bz8seD41/k18E8sChxmdL2AsxL3n+XwMf6rH9vNJnXM8e0zeJuaeP6c1w07m57XHr3Ny++HRu7l7MOje3Pmadm5e5bbWW4UeAV9z9hLvXgE8C7+lyTDdw9wl3/3zj/ixwHNjX3ajW7T3Abzbu/ybw7V2M5WbeDrzq7qe6Hchy3P1vSKuoN1tp374H+C1PPQEMm9mezkT6huVidvc/c/eo8fAJ0nnBe8YK+3kl7wE+6e5Vd38NeIX0M6ajbhazmRnwj4Hf6WhQt3CTz7iePaZXirnXj+lNQufmztO5uQV0bu4MnZs7Q+fm5W21ZHgf8HrT4zP0+InMzA4CDwHHGos+0Gjy/3gvdWtqcODPzOxpM3t/Y9lud5+A9IAFdnUtupt7L9d/KPXyfl600r7dLMf5D5BeUVx0yMy+YGZ/bWZf362gVrDc8bAZ9vPXAxfc/eWmZT21n5d8xm2KY3qZz+VFm+mY7iU99fddDZ2bO0bn5s7bTJ9jOje3ic7Nb9hqybAts6xn544ys37gD4GfcPcZ4N8Dh4EHgQnSLha95FF3fxj4FuCfm9k3dDug1TCzHPBu4Pcbi3p9P99Kzx/nZvazpPOC/3Zj0QQw7u4PAT8F/H9mNtit+JZY6Xjo+f0MfDfXf5Hsqf28zGfciqsus6wr+3qlmDfZMd1reubvuxo6N3eGzs2dt8k+x3RubhOdm6+31ZLhM8DtTY/3A+e6FMtNmVmW9I/62+7+RwDufsHdY3dPgP9AF7p93Iy7n2v8vAj8Z9L4Lix2mWj8vNi9CFf0LcDn3f0C9P5+brLSvu3p49zM3ge8C/hebwzgaHRnutK4/zTpGJ+7uxflG25yPPT6fs4A/wj43cVlvbSfl/uMo8eP6RVi3nTHdA/qib/vaujc3FE6N3fQZvsc07m5bfHp3LzEVkuGnwTuMrNDjSuO7wUe63JMN2iMJfiPwHF3/zdNy5v74f+PwPNLX9stZlYys4HF+6QD158n3b/va6z2PuC/dCfCm7ruCl0v7+clVtq3jwH/xFJvAaYXu7d0m5m9E/gg8G53Lzct32lmYeP+HcBdwInuRHm9mxwPjwHvNbO8mR0ijfnvOx3fTbwD+LK7n1lc0Cv7eaXPOHr4mL7J5/KmO6Z7kM7NbaJzc1f07OfYSjbj55jOza2nc/MKvMuVzVp9I6189hLplYCf7XY8K8T4daTdDJ4FnmncvhX4BPBcY/ljwJ5ux9oU8x2k1fu+CLywuG+BUeAzwMuNnyPdjnVJ3EXgCjDUtKzn9jPpF4IJoE56Je4HV9q3pN1WfqVxjD8HHO2hmF8hHV+yeFz/amPd72gcN18EPg98Ww/FvOLxAPxsYz+/CHxLr8TcWP6fgB9esm6v7OeVPuN69pi+Scw9fUxvlhs6N7crZp2b2xunzs3di1nn5tbHrHPzMjdrvFBERERERERk29hq3aRFREREREREbknJsIiIiIiIiGw7SoZFRERERERk21EyLCIiIiIiItuOkmERERERERHZdpQMy7ZmZm5mn2h6nDGzS2b239a5vWEz+2dNj9+23m2tsP29ZvYHrdpeJ5jZQTP7ng28/vvNbG8rYxIRkd6lc3P76dwsklIyLNvdPPAmM+trPP4m4OwGtjcM/LNbrrVO7n7O3b+zXdtvk4PAuk+4wPcDOuGKiGwfOje330F0bhZRMiwC/AnwDxv3v5t0InUAzGzEzP7YzJ41syfM7M2N5R82s4+b2eNmdsLMfqzxko8Ch83sGTP7xcayfjP7AzP7spn9tplZYxsfNbMvNbb9r5YGZWZvbWznGTP7gpkNNK7kPt94/vvN7I/M7E/N7GUz+4Wm177TzD5vZl80s880lpUaMT/Z2N57lnnPt5nZX5vZ75nZS40Yv9fM/t7MnjOzw431vs3MjjW28xdmtnulmBv75Osby37SzEIz+8VGHM+a2T9tev//vfE+X2y893cCR4Hfbry+z8ze3tj2c43fJ9947Ukz+5dm9ndm9pSZPWxmnzazV83shxvrfKL59278Pd692gNFREQ6RufmN16nc7NIu7i7brpt2xswB7wZ+AOgADwDvA34b43nfxn4ucb9bwSeadz/MPA5IA+MAVeALOmV1uebtv82YBrYT3rx6e+ArwNGgBcBa6w3vExs/xV4tHG/H8g0b5/0quwJYKgR+yngdmAn8DpwqLHeSOPnvwS+b/H9gJeA0pL3fBswBexp/G5ngf+r8dyPA/+2cX9HU+w/BPzrm8R8bX82lr8f+D8b9/PAU8Ah4Fsa+7S4JO7HgaON+4XG73Z34/FvAT/RuH8S+JHG/f8HeBYYaOyPi43lbwX+uHF/CHgNyHT7ONRNN9100+2NGzo369ysc7NuHbqpZVi2PXd/lvRE9t3Ap5Y8/XXAJxrr/SUwamZDjef+u7tX3f0ycBHYvcJb/L27n3H3hPSEfhCYASrAr5vZPwLKy7zus8C/aVzZHnb3aJl1PuPu0+5eAb4EHADeAvyNu7/WiHuyse43Az9tZs+QnsQKwPgy23zS3SfcvQq8CvxZY/lzjdgh/QLxaTN7DvjfgPvXEPM3A/+kEccxYBS4C3gH8BvuXl4Sd7N7gNfc/aXG498EvqHp+ceaYj3m7rPufgmomNmwu/81cKeZ7SL9e//hCjGKiEgX6dx8A52bRdpAybBI6jHgX9HUDavBllnXGz+rTcti0iuty7lhvcaH/CPAHwLfDvzpDW/i/lHSK7t9wBNmdu9qtt2I2ZdZ14DvcPcHG7dxdz9+i20mTY8T3vgdfxn4d+7+APBPSU/eq43ZgB9tiuOQu//ZTeJe+tqbaY516e+xGPsngO8F/hfgN26xPRER6R6dm5ffps7NIi2iZFgk9XHgI+7+3JLlf0P64YyZvQ247O4zN9nOLGn3n5sys35gyN0/BfwE8OAy6xx29+fc/edJuystd/Jazt8BbzWzQ43tjDSWfxr40aZxUQ+tcnvLGeKNYibvu0XMS/fJp4EfMbNs4zV3m1mJ9Cr3D5hZcUncza//MnDQzO5sPP6fgb9eY+z/iXSf4+4vrPG1IiLSOTo3r43OzSJrtNLVMpFtxd3PAL+0zFMfBn7DzJ4l7S71vmXWad7OFTP7bKOQxp8A/32FVQeA/2JmBdIrqj+5zDo/YWb/A+lV5S81trdnFb/LJTN7P/BHZhaQdhP7JuBfAP8WeLZx0j0JvOtW21vBh4HfN7OzwBOk44pWijkBIjP7IunJ7pdIu3R9vhHHJeDb3f1PzexB4Ckzq5F2i/s/Gq/5VTNbAL6G9Krx75tZBngS+NW1BO7uF8zsOPDH6/vVRUSkE3RuXrMPo3OzyJosDrIXEdkWGle3nwMedvfpbscjIiKy3encLN2ibtIism2Y2TtIu3P9sk62IiIi3adzs3STWoZFRERERERk21HLsIiIiIiIiGw7SoZFRERERERk21EyLCIiIiIiItuOkmERERERERHZdpQMi4iIiIiIyLbz/wNKwFhwdqbCzwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (hazard_ax, surv_ax) = plt.subplots(ncols=2, sharex=True, sharey=False, figsize=(16, 6))\n",
    "\n",
    "plot_with_hpd(interval_bounds[:-1], tv_base_hazard, cum_hazard,\n",
    "              hazard_ax, color=blue, label='Had not metastized')\n",
    "plot_with_hpd(interval_bounds[:-1], tv_met_hazard, cum_hazard,\n",
    "              hazard_ax, color=red, label='Metastized')\n",
    "\n",
    "hazard_ax.set_xlim(0, df.time.max());\n",
    "hazard_ax.set_xlabel('Months since mastectomy');\n",
    "\n",
    "hazard_ax.set_ylim(0, 2);\n",
    "hazard_ax.set_ylabel(r'Cumulative hazard $\\Lambda(t)$');\n",
    "\n",
    "hazard_ax.legend(loc=2);\n",
    "\n",
    "plot_with_hpd(interval_bounds[:-1], tv_base_hazard, survival,\n",
    "              surv_ax, color=blue)\n",
    "plot_with_hpd(interval_bounds[:-1], tv_met_hazard, survival,\n",
    "              surv_ax, color=red)\n",
    "\n",
    "surv_ax.set_xlim(0, df.time.max());\n",
    "surv_ax.set_xlabel('Months since mastectomy');\n",
    "\n",
    "surv_ax.set_ylabel('Survival function $S(t)$');\n",
    "\n",
    "fig.suptitle('Bayesian survival model with time varying effects');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We have really only scratched the surface of both survival analysis and the Bayesian approach to survival analysis.  More information on Bayesian survival analysis is available in Ibrahim et al. (2005).  (For example, we may want to account for individual frailty in either or original or time-varying models.)\n",
    "\n",
    "This tutorial is available as an [IPython](http://ipython.org/) notebook [here](https://gist.github.com/AustinRochford/4c6b07e51a2247d678d6).  It is adapted from a blog post that first appeared [here](http://austinrochford.com/posts/2015-10-05-bayes-survival.html)."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
